Wang, Luo-Hao; Huang, Wei-Xi An efficient matrix factorization within the projection framework for ameliorating the surface tension time step constraint in interfacial flows. (English) Zbl 07797657 J. Comput. Phys. 498, Article ID 112678, 15 p. (2024). MSC: 76Mxx 76Dxx 65Mxx PDFBibTeX XMLCite \textit{L.-H. Wang} and \textit{W.-X. Huang}, J. Comput. Phys. 498, Article ID 112678, 15 p. (2024; Zbl 07797657) Full Text: DOI
Ménez, L.; Parnaudeau, P.; Beringhier, M.; Goncalves Da Silva, E. Assessment of volume penalization and immersed boundary methods for compressible flows with various thermal boundary conditions. (English) Zbl 07748051 J. Comput. Phys. 493, Article ID 112465, 23 p. (2023). MSC: 76Mxx 65Mxx 76Dxx PDFBibTeX XMLCite \textit{L. Ménez} et al., J. Comput. Phys. 493, Article ID 112465, 23 p. (2023; Zbl 07748051) Full Text: DOI
Llorente, Victor J.; Kou, Jiaqing; Valero, Eusebio; Ferrer, Esteban A modified equation analysis for immersed boundary methods based on volume penalization: applications to linear advection-diffusion equations and high-order discontinuous Galerkin schemes. (English) Zbl 1521.76348 Comput. Fluids 257, Article ID 105869, 16 p. (2023). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{V. J. Llorente} et al., Comput. Fluids 257, Article ID 105869, 16 p. (2023; Zbl 1521.76348) Full Text: DOI arXiv
Basarić, Danica; Feireisl, Eduard; Lukáčová-Medvid’ová, Mária; Mizerová, Hana; Yuan, Yuhuan Penalization method for the Navier-Stokes-Fourier system. (English) Zbl 1501.35307 ESAIM, Math. Model. Numer. Anal. 56, No. 6, 1911-1938 (2022). MSC: 35Q35 35A01 76N06 76M12 PDFBibTeX XMLCite \textit{D. Basarić} et al., ESAIM, Math. Model. Numer. Anal. 56, No. 6, 1911--1938 (2022; Zbl 1501.35307) Full Text: DOI arXiv
Lai, Ming-Chih; Chang, Che-Chia; Lin, Wei-Syuan; Hu, Wei-Fan; Lin, Te-Sheng A shallow Ritz method for elliptic problems with singular sources. (English) Zbl 07592144 J. Comput. Phys. 469, Article ID 111547, 14 p. (2022). MSC: 65Nxx 35Jxx 76Mxx PDFBibTeX XMLCite \textit{M.-C. Lai} et al., J. Comput. Phys. 469, Article ID 111547, 14 p. (2022; Zbl 07592144) Full Text: DOI arXiv
Cao, Fujun; Yuan, Dongfang; Sheng, Zhiqiang; Yuan, Guangwei; He, Limin A finite difference method for elliptic problems with implicit jump condition. (English) Zbl 1513.65276 Int. J. Numer. Anal. Model. 19, No. 4, 439-457 (2022). MSC: 65N06 35R35 35J65 PDFBibTeX XMLCite \textit{F. Cao} et al., Int. J. Numer. Anal. Model. 19, No. 4, 439--457 (2022; Zbl 1513.65276) Full Text: Link
Laymuns, Genaro; Sánchez, Manuel A. Corrected finite element methods on unfitted meshes for Stokes moving interface problem. (English) Zbl 1524.65832 Comput. Math. Appl. 108, 159-174 (2022). MSC: 65N30 35J25 65N15 74F10 65N50 76D07 65M60 65M06 92C35 35Q92 74B10 76M10 74S05 35Q35 35Q74 PDFBibTeX XMLCite \textit{G. Laymuns} and \textit{M. A. Sánchez}, Comput. Math. Appl. 108, 159--174 (2022; Zbl 1524.65832) Full Text: DOI
Zhou, Kun; Balachandar, S. An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing. (English) Zbl 07508467 J. Comput. Phys. 424, Article ID 109862, 29 p. (2021). MSC: 76-XX 74-XX PDFBibTeX XMLCite \textit{K. Zhou} and \textit{S. Balachandar}, J. Comput. Phys. 424, Article ID 109862, 29 p. (2021; Zbl 07508467) Full Text: DOI
Constant, Benjamin; Péron, Stéphanie; Beaugendre, Héloïse; Benoit, Christophe An improved immersed boundary method for turbulent flow simulations on Cartesian grids. (English) Zbl 07503726 J. Comput. Phys. 435, Article ID 110240, 21 p. (2021). MSC: 76Mxx 65Mxx 76Dxx PDFBibTeX XMLCite \textit{B. Constant} et al., J. Comput. Phys. 435, Article ID 110240, 21 p. (2021; Zbl 07503726) Full Text: DOI HAL
Vahab, Mehdi; Sussman, Mark; Shoele, Kourosh Fluid-structure interaction of thin flexible bodies in multi-material multi-phase systems. (English) Zbl 07500743 J. Comput. Phys. 429, Article ID 110008, 29 p. (2021). MSC: 76Mxx 76Txx 65Mxx PDFBibTeX XMLCite \textit{M. Vahab} et al., J. Comput. Phys. 429, Article ID 110008, 29 p. (2021; Zbl 07500743) Full Text: DOI
Harikrishnan, B.; Chen, Zhen; Shu, Chang A new explicit immersed boundary method for simulation of fluid-solid interactions. (English) Zbl 1488.35422 Adv. Appl. Math. Mech. 13, No. 2, 261-284 (2021). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{B. Harikrishnan} et al., Adv. Appl. Math. Mech. 13, No. 2, 261--284 (2021; Zbl 1488.35422) Full Text: DOI
Péron, S.; Renaud, T.; Benoit, C.; Mary, I. An immersed boundary method on Cartesian adaptive grids for the simulation of compressible flows. (English) Zbl 1464.76072 Deiterding, Ralf (ed.) et al., Cartesian CFD methods for complex applications. Selected papers based on the presentations of the mini-symposium at ICIAM 2019, Valencia, Spain, July 14–19, 2019. Cham: Springer. SEMA SIMAI Springer Ser. ICIAM 2019 SEMA SIMAI Springer Ser. 3, 67-91 (2021). MSC: 76M12 76N06 76J20 76F65 76F50 PDFBibTeX XMLCite \textit{S. Péron} et al., SEMA SIMAI Springer Ser. ICIAM 2019 SEMA SIMAI Springer Ser. 3, 67--91 (2021; Zbl 1464.76072) Full Text: DOI
Dorschner, Benedikt; Colonius, Tim Immersed boundary projection methods. (English) Zbl 1512.76062 Roy, Somnath (ed.) et al., Immersed boundary method. Development and applications. Singapore: Springer. Comput. Methods Eng. Sci., 3-43 (2020). MSC: 76M12 76M99 76D05 76-02 PDFBibTeX XMLCite \textit{B. Dorschner} and \textit{T. Colonius}, in: Immersed boundary method. Development and applications. Singapore: Springer. 3--43 (2020; Zbl 1512.76062) Full Text: DOI
Tschisgale, Silvio; Fröhlich, Jochen An immersed boundary method for the fluid-structure interaction of slender flexible structures in viscous fluid. (English) Zbl 07508416 J. Comput. Phys. 423, Article ID 109801, 27 p. (2020). MSC: 74-XX 92-XX PDFBibTeX XMLCite \textit{S. Tschisgale} and \textit{J. Fröhlich}, J. Comput. Phys. 423, Article ID 109801, 27 p. (2020; Zbl 07508416) Full Text: DOI arXiv
Amiri, Farhad A.; Le, Guigao; Chen, Qing; Zhang, Junfeng Accuracy improvement for immersed boundary method using Lagrangian velocity interpolation. (English) Zbl 07508415 J. Comput. Phys. 423, Article ID 109800, 23 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{F. A. Amiri} et al., J. Comput. Phys. 423, Article ID 109800, 23 p. (2020; Zbl 07508415) Full Text: DOI
Becerra-Sagredo, Julián T.; Jeltsch, Rolf; Málaga, Carlos The collocation basis of compact finite differences for moment-preserving interpolations: review, extension and applications. (English) Zbl 1482.65018 Commun. Comput. Phys. 28, No. 4, 1245-1273 (2020). MSC: 65D05 65D07 41A05 76M23 PDFBibTeX XMLCite \textit{J. T. Becerra-Sagredo} et al., Commun. Comput. Phys. 28, No. 4, 1245--1273 (2020; Zbl 1482.65018) Full Text: DOI
Wang, Luohao; Xie, Chunmei; Huang, Weixi A monolithic projection framework for constrained FSI problems with the immersed boundary method. (English) Zbl 1506.74113 Comput. Methods Appl. Mech. Eng. 371, Article ID 113332, 36 p. (2020). MSC: 74F10 74S15 65M38 76D05 PDFBibTeX XMLCite \textit{L. Wang} et al., Comput. Methods Appl. Mech. Eng. 371, Article ID 113332, 36 p. (2020; Zbl 1506.74113) Full Text: DOI
Kwon, Chunsong; Tartakovsky, Daniel M. Modified immersed boundary method for flows over randomly rough surfaces. (English) Zbl 1453.76035 J. Comput. Phys. 406, Article ID 109195, 16 p. (2020). MSC: 76D05 76M20 35R60 65M06 76D07 PDFBibTeX XMLCite \textit{C. Kwon} and \textit{D. M. Tartakovsky}, J. Comput. Phys. 406, Article ID 109195, 16 p. (2020; Zbl 1453.76035) Full Text: DOI
Rycroft, Chris H.; Wu, Chen-Hung; Yu, Yue; Kamrin, Ken Reference map technique for incompressible fluid-structure interaction. (English) Zbl 1460.76177 J. Fluid Mech. 898, Paper No. A9, 44 p. (2020). MSC: 76D05 74F10 PDFBibTeX XMLCite \textit{C. H. Rycroft} et al., J. Fluid Mech. 898, Paper No. A9, 44 p. (2020; Zbl 1460.76177) Full Text: DOI arXiv
Qin, Zhipeng; Riaz, Amir; Balaras, Elias A locally second order symmetric method for discontinuous solution of Poisson’s equation on uniform Cartesian grids. (English) Zbl 1519.76345 Comput. Fluids 198, Article ID 104397, 14 p. (2020). MSC: 76T99 65N06 PDFBibTeX XMLCite \textit{Z. Qin} et al., Comput. Fluids 198, Article ID 104397, 14 p. (2020; Zbl 1519.76345) Full Text: DOI
Bharadwaj S., Anand; Ghosh, Santanu Data reconstruction at surface in immersed-boundary methods. (English) Zbl 1519.76201 Comput. Fluids 196, Article ID 104236, 17 p. (2020). MSC: 76M20 76M15 PDFBibTeX XMLCite \textit{A. Bharadwaj S.} and \textit{S. Ghosh}, Comput. Fluids 196, Article ID 104236, 17 p. (2020; Zbl 1519.76201) Full Text: DOI
Allen, T.; Zerroukat, M. A semi-Lagrangian semi-implicit immersed boundary method for atmospheric flow over complex terrain. (English) Zbl 1453.86021 J. Comput. Phys. 397, Article ID 108857, 13 p. (2019). MSC: 86A10 65M22 86-08 PDFBibTeX XMLCite \textit{T. Allen} and \textit{M. Zerroukat}, J. Comput. Phys. 397, Article ID 108857, 13 p. (2019; Zbl 1453.86021) Full Text: DOI
Ma, Yunfei; Cui, Jiahuan; Vadlamani, Nagabhushana Rao; Tucker, Paul Hierarchical geometry modelling using the immersed boundary method. (English) Zbl 1441.76066 Comput. Methods Appl. Mech. Eng. 355, 323-348 (2019). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{Y. Ma} et al., Comput. Methods Appl. Mech. Eng. 355, 323--348 (2019; Zbl 1441.76066) Full Text: DOI
Abdol Azis, Mohd Hazmil; Evrard, Fabien; van Wachem, Berend An immersed boundary method for incompressible flows in complex domains. (English) Zbl 1454.76058 J. Comput. Phys. 378, 770-795 (2019). MSC: 76M12 74F10 PDFBibTeX XMLCite \textit{M. H. Abdol Azis} et al., J. Comput. Phys. 378, 770--795 (2019; Zbl 1454.76058) Full Text: DOI
So, R. M. C.; Leung, R. C. K.; Kam, E. W. S.; Fu, S. C. Progress in the development of a new lattice Boltzmann method. (English) Zbl 1496.76104 Comput. Fluids 190, 440-469 (2019). MSC: 76M28 76P05 PDFBibTeX XMLCite \textit{R. M. C. So} et al., Comput. Fluids 190, 440--469 (2019; Zbl 1496.76104) Full Text: DOI
Hu, Zhicheng Numerical investigation of heat conduction with multiple moving heat sources. (English) Zbl 1425.80011 Symmetry 10, No. 12, Paper No. 673, 15 p. (2018). MSC: 80M25 PDFBibTeX XMLCite \textit{Z. Hu}, Symmetry 10, No. 12, Paper No. 673, 15 p. (2018; Zbl 1425.80011) Full Text: DOI arXiv
Riahi, H.; Meldi, M.; Favier, J.; Serre, E.; Goncalves, E. A pressure-corrected immersed boundary method for the numerical simulation of compressible flows. (English) Zbl 1416.76226 J. Comput. Phys. 374, 361-383 (2018). MSC: 76M25 76N15 PDFBibTeX XMLCite \textit{H. Riahi} et al., J. Comput. Phys. 374, 361--383 (2018; Zbl 1416.76226) Full Text: DOI HAL
Tschisgale, Silvio; Kempe, Tobias; Fröhlich, Jochen A general implicit direct forcing immersed boundary method for rigid particles. (English) Zbl 1410.76049 Comput. Fluids 170, 285-298 (2018). MSC: 76D05 74F10 76-04 76M12 PDFBibTeX XMLCite \textit{S. Tschisgale} et al., Comput. Fluids 170, 285--298 (2018; Zbl 1410.76049) Full Text: DOI
Mittal, H. V. R.; Ray, Rajendra K. Solving immersed interface problems using a new interfacial points-based finite difference approach. (English) Zbl 1448.65195 SIAM J. Sci. Comput. 40, No. 3, A1860-A1883 (2018). MSC: 65N06 52B10 68U05 68U07 65D18 65D05 76M20 76D07 35Q35 35R05 PDFBibTeX XMLCite \textit{H. V. R. Mittal} and \textit{R. K. Ray}, SIAM J. Sci. Comput. 40, No. 3, A1860--A1883 (2018; Zbl 1448.65195) Full Text: DOI
Kim, Woojin; Lee, Injae; Choi, Haecheon A weak-coupling immersed boundary method for fluid-structure interaction with low density ratio of solid to fluid. (English) Zbl 1383.74086 J. Comput. Phys. 359, 296-311 (2018). MSC: 74S05 74F10 76M10 PDFBibTeX XMLCite \textit{W. Kim} et al., J. Comput. Phys. 359, 296--311 (2018; Zbl 1383.74086) Full Text: DOI
Liska, Sebastian; Colonius, Tim A fast immersed boundary method for external incompressible viscous flows using lattice Green’s functions. (English) Zbl 1378.76083 J. Comput. Phys. 331, 257-279 (2017). MSC: 76M25 76D05 76D17 PDFBibTeX XMLCite \textit{S. Liska} and \textit{T. Colonius}, J. Comput. Phys. 331, 257--279 (2017; Zbl 1378.76083) Full Text: DOI arXiv Link
Rowlatt, C. F.; Phillips, T. N. A spectral element formulation of the immersed boundary method for Newtonian fluids. (English) Zbl 1423.74949 Comput. Methods Appl. Mech. Eng. 298, 29-57 (2016). MSC: 74S25 74S05 74S15 65M70 65M60 74F10 PDFBibTeX XMLCite \textit{C. F. Rowlatt} and \textit{T. N. Phillips}, Comput. Methods Appl. Mech. Eng. 298, 29--57 (2016; Zbl 1423.74949) Full Text: DOI
Kumar, Manish; Roy, Somnath A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation. (English) Zbl 1390.76585 Comput. Fluids 137, 15-35 (2016). MSC: 76M20 65M06 76D05 PDFBibTeX XMLCite \textit{M. Kumar} and \textit{S. Roy}, Comput. Fluids 137, 15--35 (2016; Zbl 1390.76585) Full Text: DOI
Feldman, Yuri; Gulberg, Yosef An extension of the immersed boundary method based on the distributed Lagrange multiplier approach. (English) Zbl 1351.76105 J. Comput. Phys. 322, 248-266 (2016). MSC: 76M12 65M08 76D05 PDFBibTeX XMLCite \textit{Y. Feldman} and \textit{Y. Gulberg}, J. Comput. Phys. 322, 248--266 (2016; Zbl 1351.76105) Full Text: DOI
Hosseini, Bamdad; Nigam, Nilima; Stockie, John M. On regularizations of the Dirac delta distribution. (English) Zbl 1349.35008 J. Comput. Phys. 305, 423-447 (2016). MSC: 35A35 35A08 PDFBibTeX XMLCite \textit{B. Hosseini} et al., J. Comput. Phys. 305, 423--447 (2016; Zbl 1349.35008) Full Text: DOI arXiv
Maertens, Audrey P.; Weymouth, Gabriel D. Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers. (English) Zbl 1423.76180 Comput. Methods Appl. Mech. Eng. 283, 106-129 (2015). MSC: 76G25 74F10 76M20 PDFBibTeX XMLCite \textit{A. P. Maertens} and \textit{G. D. Weymouth}, Comput. Methods Appl. Mech. Eng. 283, 106--129 (2015; Zbl 1423.76180) Full Text: DOI Link
Frisani, Angelo; Hassan, Yassin A. On the immersed boundary method: finite element versus finite volume approach. (English) Zbl 1390.65105 Comput. Fluids 121, 51-67 (2015). MSC: 65M60 65M08 76M10 76M12 PDFBibTeX XMLCite \textit{A. Frisani} and \textit{Y. A. Hassan}, Comput. Fluids 121, 51--67 (2015; Zbl 1390.65105) Full Text: DOI
Nicolaou, L.; Jung, S. Y.; Zaki, T. A. A robust direct-forcing immersed boundary method with enhanced stability for moving body problems in curvilinear coordinates. (English) Zbl 1390.76603 Comput. Fluids 119, 101-114 (2015). MSC: 76M20 65M06 76D05 PDFBibTeX XMLCite \textit{L. Nicolaou} et al., Comput. Fluids 119, 101--114 (2015; Zbl 1390.76603) Full Text: DOI Link
van Nimwegen, A. T.; Schutte, K. C. J.; Portela, L. M. Direct numerical simulation of turbulent flow in pipes with an arbitrary roughness topography using a combined momentum-mass source immersed boundary method. (English) Zbl 1390.76249 Comput. Fluids 108, 92-106 (2015). MSC: 76F65 76M12 PDFBibTeX XMLCite \textit{A. T. van Nimwegen} et al., Comput. Fluids 108, 92--106 (2015; Zbl 1390.76249) Full Text: DOI
Benvenuti, Elena; Ventura, Giulio; Ponara, Nicola; Tralli, Antonio Accuracy of three-dimensional analysis of regularized singularities. (English) Zbl 1352.65080 Int. J. Numer. Methods Eng. 101, No. 1, 29-53 (2015). MSC: 65D30 PDFBibTeX XMLCite \textit{E. Benvenuti} et al., Int. J. Numer. Methods Eng. 101, No. 1, 29--53 (2015; Zbl 1352.65080) Full Text: DOI
Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe A Luenberger observer for reaction-diffusion models with front position data. (English) Zbl 1349.76445 J. Comput. Phys. 300, 288-307 (2015). MSC: 76M20 35K58 35K20 35K57 65M06 94A08 PDFBibTeX XMLCite \textit{A. Collin} et al., J. Comput. Phys. 300, 288--307 (2015; Zbl 1349.76445) Full Text: DOI
Li, Zhilin; Wang, Li; Aspinwall, Eric; Cooper, Racheal; Kuberry, Paul; Sanders, Ashley; Zeng, Ke Some new analysis results for a class of interface problems. (English) Zbl 1338.65197 Math. Methods Appl. Sci. 38, No. 18, 4530-4539 (2015). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 65L10 34A36 65L20 34B16 PDFBibTeX XMLCite \textit{Z. Li} et al., Math. Methods Appl. Sci. 38, No. 18, 4530--4539 (2015; Zbl 1338.65197) Full Text: DOI Link
Li, Zhilin On convergence of the immersed boundary method for elliptic interface problems. (English) Zbl 1311.65133 Math. Comput. 84, No. 293, 1169-1188 (2015). MSC: 65N06 65N12 65N15 PDFBibTeX XMLCite \textit{Z. Li}, Math. Comput. 84, No. 293, 1169--1188 (2015; Zbl 1311.65133) Full Text: DOI
Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. (English) Zbl 1290.65110 Math. Comput. 83, No. 286, 665-699 (2014). Reviewer: Petr Sváček (Praha) MSC: 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{B. Cockburn} et al., Math. Comput. 83, No. 286, 665--699 (2014; Zbl 1290.65110) Full Text: DOI
Gibou, Frédéric; Min, Chohong; Fedkiw, Ron High resolution sharp computational methods for elliptic and parabolic problems in complex geometries. (English) Zbl 1263.65093 J. Sci. Comput. 54, No. 2-3, 369-413 (2013). MSC: 65M50 35J05 35K05 80A22 65N50 35R35 65M06 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Sci. Comput. 54, No. 2--3, 369--413 (2013; Zbl 1263.65093) Full Text: DOI
Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong Immersed smoothed finite element method for two dimensional fluid-structure interaction problems. (English) Zbl 1242.74178 Int. J. Numer. Methods Eng. 90, No. 10, 1292-1320 (2012). MSC: 74S05 76M10 74F10 76D05 PDFBibTeX XMLCite \textit{Z.-Q. Zhang} et al., Int. J. Numer. Methods Eng. 90, No. 10, 1292--1320 (2012; Zbl 1242.74178) Full Text: DOI
Fang, Jiannong; Diebold, Marc; Higgins, Chad; Parlange, Marc B. Towards oscillation-free implementation of the immersed boundary method with spectral-like methods. (English) Zbl 1408.76412 J. Comput. Phys. 230, No. 22, 8179-8191 (2011). MSC: 76M28 65M70 65M85 76D05 PDFBibTeX XMLCite \textit{J. Fang} et al., J. Comput. Phys. 230, No. 22, 8179--8191 (2011; Zbl 1408.76412) Full Text: DOI Link
Xu, Sheng A boundary condition capturing immersed interface method for 3D rigid objects in a flow. (English) Zbl 1408.76172 J. Comput. Phys. 230, No. 19, 7176-7190 (2011). MSC: 76D05 76M25 PDFBibTeX XMLCite \textit{S. Xu}, J. Comput. Phys. 230, No. 19, 7176--7190 (2011; Zbl 1408.76172) Full Text: DOI
Chen, Kuan-Yu; Feng, Ko-An; Kim, Yongsam; Lai, Ming-Chih A note on pressure accuracy in immersed boundary method for Stokes flow. (English) Zbl 1416.76098 J. Comput. Phys. 230, No. 12, 4377-4383 (2011). MSC: 76M10 76D07 65N06 65N85 PDFBibTeX XMLCite \textit{K.-Y. Chen} et al., J. Comput. Phys. 230, No. 12, 4377--4383 (2011; Zbl 1416.76098) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a reaction–diffusion system with a control discrete source term. (English) Zbl 1210.65150 Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186-197 (2011). MSC: 65M06 35K57 65K10 65M12 49J20 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186--197 (2011; Zbl 1210.65150) Full Text: DOI
Li, Zhilin; Lai, Ming-Chih; He, Guowei; Zhao, Hongkai An augmented method for free boundary problems with moving contact lines. (English) Zbl 1242.76047 Comput. Fluids 39, No. 6, 1033-1040 (2010). MSC: 76D27 76D45 76M25 76M20 PDFBibTeX XMLCite \textit{Z. Li} et al., Comput. Fluids 39, No. 6, 1033--1040 (2010; Zbl 1242.76047) Full Text: DOI Link
Sudhakar, Y.; Vengadesan, S. Flight force production by flapping insect wings in inclined stroke plane kinematics. (English) Zbl 1242.76379 Comput. Fluids 39, No. 4, 683-695 (2010). MSC: 76Z10 92C10 PDFBibTeX XMLCite \textit{Y. Sudhakar} and \textit{S. Vengadesan}, Comput. Fluids 39, No. 4, 683--695 (2010; Zbl 1242.76379) Full Text: DOI
Pinelli, A.; Naqavi, I. Z.; Piomelli, U.; Favier, J. Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. (English) Zbl 1427.76053 J. Comput. Phys. 229, No. 24, 9073-9091 (2010). MSC: 76D05 76M20 76M12 PDFBibTeX XMLCite \textit{A. Pinelli} et al., J. Comput. Phys. 229, No. 24, 9073--9091 (2010; Zbl 1427.76053) Full Text: DOI
Gong, Zhao-xin; Lu, Chuan-jing; Huang, Hua-xiong Accuracy analysis of immersed boundary method using method of manufactured solutions. (English) Zbl 1410.76326 Appl. Math. Mech., Engl. Ed. 31, No. 10, 1197-1208 (2010). MSC: 76M25 65N12 76M15 PDFBibTeX XMLCite \textit{Z.-x. Gong} et al., Appl. Math. Mech., Engl. Ed. 31, No. 10, 1197--1208 (2010; Zbl 1410.76326) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a diffusion equation with a discrete source term. (English) Zbl 1204.65100 Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176-1187 (2010). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35K05 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176--1187 (2010; Zbl 1204.65100) Full Text: DOI Link
Zahedi, Sara; Tornberg, Anna-Karin Delta function approximations in level set methods by distance function extension. (English) Zbl 1186.65018 J. Comput. Phys. 229, No. 6, 2199-2219 (2010). MSC: 65D15 PDFBibTeX XMLCite \textit{S. Zahedi} and \textit{A.-K. Tornberg}, J. Comput. Phys. 229, No. 6, 2199--2219 (2010; Zbl 1186.65018) Full Text: DOI
Guy, Robert D.; Hartenstine, David A. On the accuracy of direct forcing immersed boundary methods with projection methods. (English) Zbl 1423.76337 J. Comput. Phys. 229, No. 7, 2479-2496 (2010). MSC: 76M25 35Q30 PDFBibTeX XMLCite \textit{R. D. Guy} and \textit{D. A. Hartenstine}, J. Comput. Phys. 229, No. 7, 2479--2496 (2010; Zbl 1423.76337) Full Text: DOI
Yang, Xiaolei; Zhang, Xing; Li, Zhilin; He, Guo-Wei A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. (English) Zbl 1391.76590 J. Comput. Phys. 228, No. 20, 7821-7836 (2009). MSC: 76M25 65N99 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Comput. Phys. 228, No. 20, 7821--7836 (2009; Zbl 1391.76590) Full Text: DOI
Towers, John D. Discretizing delta functions via finite differences and gradient normalization. (English) Zbl 1167.65007 J. Comput. Phys. 228, No. 10, 3816-3836 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D15 46F10 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 10, 3816--3836 (2009; Zbl 1167.65007) Full Text: DOI
Chen, Wan; Ward, Michael J. Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional Gray-Scott model. (English) Zbl 1197.35021 Eur. J. Appl. Math. 20, No. 2, 187-214 (2009). Reviewer: Denise Huet (Nancy) MSC: 35B25 35K57 80A22 35B32 35Q79 PDFBibTeX XMLCite \textit{W. Chen} and \textit{M. J. Ward}, Eur. J. Appl. Math. 20, No. 2, 187--214 (2009; Zbl 1197.35021) Full Text: DOI
Luo, Xian; Maxey, Martin R.; Karniadakis, George Em Smoothed profile method for particulate flows: error analysis and simulations. (English) Zbl 1409.76102 J. Comput. Phys. 228, No. 5, 1750-1769 (2009). MSC: 76M25 76T20 PDFBibTeX XMLCite \textit{X. Luo} et al., J. Comput. Phys. 228, No. 5, 1750--1769 (2009; Zbl 1409.76102) Full Text: DOI
Liu, Hailiang; Wang, Zhongming Superposition of multi-valued solutions in high frequency wave dynamics. (English) Zbl 1203.65141 J. Sci. Comput. 35, No. 2-3, 192-218 (2008). MSC: 65M06 35F20 76M25 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Z. Wang}, J. Sci. Comput. 35, No. 2--3, 192--218 (2008; Zbl 1203.65141) Full Text: DOI
Ramière, Isabelle Convergence analysis of the \(\mathcal {Q}_{1}\)-finite element method for elliptic problems with non-boundary-fitted meshes. (English) Zbl 1195.65154 Int. J. Numer. Methods Eng. 75, No. 9, 1007-1052 (2008). MSC: 65N12 65N15 65N30 PDFBibTeX XMLCite \textit{I. Ramière}, Int. J. Numer. Methods Eng. 75, No. 9, 1007--1052 (2008; Zbl 1195.65154) Full Text: DOI
Vos, P. E. J.; van Loon, R.; Sherwin, S. J. A comparison of fictitious domain methods appropriate for spectral/\(hp\) element discretisations. (English) Zbl 1158.76357 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2275-2289 (2008). MSC: 76M10 76M22 74F10 PDFBibTeX XMLCite \textit{P. E. J. Vos} et al., Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2275--2289 (2008; Zbl 1158.76357) Full Text: DOI
Colonius, Tim; Taira, Kunihiko A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions. (English) Zbl 1158.76395 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2131-2146 (2008). MSC: 76M25 76D05 76M12 PDFBibTeX XMLCite \textit{T. Colonius} and \textit{K. Taira}, Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2131--2146 (2008; Zbl 1158.76395) Full Text: DOI
Xu, Sheng; Wang, Z. Jane A 3D immersed interface method for fluid-solid interaction. (English) Zbl 1158.74540 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2068-2086 (2008). MSC: 74S30 74F10 76D05 PDFBibTeX XMLCite \textit{S. Xu} and \textit{Z. J. Wang}, Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2068--2086 (2008; Zbl 1158.74540) Full Text: DOI
Liehr, Florian; Preusser, Tobias; Rumpf, Martin; Sauter, Stefan; Schwen, Lars Ole Composite finite elements for 3D image based computing. (English) Zbl 1512.65036 Comput. Vis. Sci. 12, No. 4, 171-188 (2009). MSC: 65D18 68U10 92C55 94A08 PDFBibTeX XMLCite \textit{F. Liehr} et al., Comput. Vis. Sci. 12, No. 4, 171--188 (2008; Zbl 1512.65036) Full Text: DOI
Wang, Zeli; Fan, Jianren; Luo, Kun Parallel computing strategy for the simulation of particulate flows with immersed boundary method. (English) Zbl 1143.76049 Sci. China, Ser. E 51, No. 8, 1169-1176 (2008). MSC: 76M25 76T20 65Y05 PDFBibTeX XMLCite \textit{Z. Wang} et al., Sci. China, Ser. E 51, No. 8, 1169--1176 (2008; Zbl 1143.76049) Full Text: DOI
Liang, An; Jing, Xiaodong; Sun, Xiaofeng Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions. (English) Zbl 1147.65098 J. Comput. Phys. 227, No. 18, 8341-8366 (2008). MSC: 65N35 35J25 65N06 65L60 65L12 34B05 PDFBibTeX XMLCite \textit{A. Liang} et al., J. Comput. Phys. 227, No. 18, 8341--8366 (2008; Zbl 1147.65098) Full Text: DOI
Mori, Yoichiro Convergence proof of the velocity field for a Stokes flow immersed boundary method. (English) Zbl 1171.76042 Commun. Pure Appl. Math. 61, No. 9, 1213-1263 (2008). Reviewer: Tomislav Zlatanovski (Skopje) MSC: 76M22 76M20 76D07 74F10 65M12 65N12 PDFBibTeX XMLCite \textit{Y. Mori}, Commun. Pure Appl. Math. 61, No. 9, 1213--1263 (2008; Zbl 1171.76042) Full Text: DOI
Su, Shen-Wei; Lai, Ming-Chih; Lin, Chao-An An immersed boundary technique for simulating complex flows with rigid boundary. (English) Zbl 1177.76299 Comput. Fluids 36, No. 2, 313-324 (2007). MSC: 76M25 76D05 PDFBibTeX XMLCite \textit{S.-W. Su} et al., Comput. Fluids 36, No. 2, 313--324 (2007; Zbl 1177.76299) Full Text: DOI
Boffi, Daniele; Gastaldi, Lucia; Heltai, Luca Numerical stability of the finite element immersed boundary method. (English) Zbl 1186.76661 Math. Models Methods Appl. Sci. 17, No. 10, 1479-1505 (2007). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 76M10 76D05 74F10 65N12 65N30 PDFBibTeX XMLCite \textit{D. Boffi} et al., Math. Models Methods Appl. Sci. 17, No. 10, 1479--1505 (2007; Zbl 1186.76661) Full Text: DOI
Wen, Xin High order numerical methods to a type of delta function integrals. (English) Zbl 1125.65024 J. Comput. Phys. 226, No. 2, 1952-1967 (2007). MSC: 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{X. Wen}, J. Comput. Phys. 226, No. 2, 1952--1967 (2007; Zbl 1125.65024) Full Text: DOI
Hou, Thomas Y.; Li, Ruo Computing nearly singular solutions using pseudo-spectral methods. (English) Zbl 1310.76127 J. Comput. Phys. 226, No. 1, 379-397 (2007). MSC: 76M22 65M70 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{R. Li}, J. Comput. Phys. 226, No. 1, 379--397 (2007; Zbl 1310.76127) Full Text: DOI arXiv Link
Taira, Kunihiko; Colonius, Tim The immersed boundary method: a projection approach. (English) Zbl 1343.76027 J. Comput. Phys. 225, No. 2, 2118-2137 (2007). MSC: 76M12 76M25 76D05 PDFBibTeX XMLCite \textit{K. Taira} and \textit{T. Colonius}, J. Comput. Phys. 225, No. 2, 2118--2137 (2007; Zbl 1343.76027) Full Text: DOI
Zhong, Xiaolin A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity. (English) Zbl 1343.65130 J. Comput. Phys. 225, No. 1, 1066-1099 (2007). MSC: 65N06 76M20 76T99 PDFBibTeX XMLCite \textit{X. Zhong}, J. Comput. Phys. 225, No. 1, 1066--1099 (2007; Zbl 1343.65130) Full Text: DOI
Liu, Hailiang; Wang, Zhongming A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. (English) Zbl 1140.81399 J. Comput. Phys. 225, No. 1, 591-614 (2007). Reviewer: Nina Shokina (Freiburg) MSC: 81Q20 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Z. Wang}, J. Comput. Phys. 225, No. 1, 591--614 (2007; Zbl 1140.81399) Full Text: DOI
Towers, John D. Two methods for discretizing a delta function supported on a level set. (English) Zbl 1115.65028 J. Comput. Phys. 220, No. 2, 915-931 (2007). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 58C35 46F10 41A55 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 220, No. 2, 915--931 (2007; Zbl 1115.65028) Full Text: DOI
Cristallo, Antonio; Verzicco, Roberto Combined immersed boundary/large eddy simulations of incompressible three-dimensional complex flows. (English) Zbl 1106.76037 Flow Turbul. Combust. 77, No. 1-4, 3-26 (2006). MSC: 76F65 76M25 PDFBibTeX XMLCite \textit{A. Cristallo} and \textit{R. Verzicco}, Flow Turbul. Combust. 77, No. 1--4, 3--26 (2006; Zbl 1106.76037) Full Text: DOI
Xu, Sheng; Wang, Z. Jane An immersed interface method for simulating the interaction of a fluid with moving boundaries. (English) Zbl 1220.76058 J. Comput. Phys. 216, No. 2, 454-493 (2006). MSC: 76M25 65M60 74F10 76M20 PDFBibTeX XMLCite \textit{S. Xu} and \textit{Z. J. Wang}, J. Comput. Phys. 216, No. 2, 454--493 (2006; Zbl 1220.76058) Full Text: DOI
Smereka, Peter The numerical approximation of a delta function with application to level set methods. (English) Zbl 1086.65503 J. Comput. Phys. 211, No. 1, 77-90 (2006). MSC: 65D15 65L10 34B05 35J05 65N06 PDFBibTeX XMLCite \textit{P. Smereka}, J. Comput. Phys. 211, No. 1, 77--90 (2006; Zbl 1086.65503) Full Text: DOI
Engquist, Björn; Tornberg, Anna-Karin; Tsai, Richard Discretization of Dirac delta functions in level set methods. (English) Zbl 1074.65025 J. Comput. Phys. 207, No. 1, 28-51 (2005). Reviewer: Nácere Hayek (La Laguna) MSC: 65D20 46F10 PDFBibTeX XMLCite \textit{B. Engquist} et al., J. Comput. Phys. 207, No. 1, 28--51 (2005; Zbl 1074.65025) Full Text: DOI
Linnick, Mark N.; Fasel, Hermann F. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. (English) Zbl 1143.76538 J. Comput. Phys. 204, No. 1, 157-192 (2005). MSC: 76M25 65M06 PDFBibTeX XMLCite \textit{M. N. Linnick} and \textit{H. F. Fasel}, J. Comput. Phys. 204, No. 1, 157--192 (2005; Zbl 1143.76538) Full Text: DOI
Kandilarov, Juri D.; Vulkov, Lubin G. The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions. (English) Zbl 1074.65102 Numer. Algorithms 36, No. 4, 285-307 (2004). Reviewer: Marek Brandner (Plzeň) MSC: 65M06 35K57 80A32 80M20 PDFBibTeX XMLCite \textit{J. D. Kandilarov} and \textit{L. G. Vulkov}, Numer. Algorithms 36, No. 4, 285--307 (2004; Zbl 1074.65102) Full Text: DOI
Tornberg, Anna-Karin; Engquist, Björn Numerical approximations of singular source terms in differential equations. (English) Zbl 1115.76392 J. Comput. Phys. 200, No. 2, 462-488 (2004). MSC: 76M25 74S30 65N99 PDFBibTeX XMLCite \textit{A.-K. Tornberg} and \textit{B. Engquist}, J. Comput. Phys. 200, No. 2, 462--488 (2004; Zbl 1115.76392) Full Text: DOI
Berthelsen, Petter Andreas A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. (English) Zbl 1052.65100 J. Comput. Phys. 197, No. 1, 364-386 (2004). MSC: 65N06 35J25 35R05 PDFBibTeX XMLCite \textit{P. A. Berthelsen}, J. Comput. Phys. 197, No. 1, 364--386 (2004; Zbl 1052.65100) Full Text: DOI
Jin, Shi; Wang, Xuelei Robust numerical simulation of porosity evolution in chemical vapor infiltration. II: Two-dimensional anisotropic fronts. (English) Zbl 1130.76385 J. Comput. Phys. 179, No. 2, 557-577 (2002). MSC: 76M20 76V05 76S05 80A30 76T30 PDFBibTeX XMLCite \textit{S. Jin} and \textit{X. Wang}, J. Comput. Phys. 179, No. 2, 557--577 (2002; Zbl 1130.76385) Full Text: DOI
Gibou, Frederic; Fedkiw, Ronald P.; Cheng, Li-Tien; Kang, Myungjoo A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. (English) Zbl 0996.65108 J. Comput. Phys. 176, No. 1, 205-227 (2002). MSC: 65N06 65M06 35K05 35R35 35J05 80M20 80A22 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Comput. Phys. 176, No. 1, 205--227 (2002; Zbl 0996.65108) Full Text: DOI Link
Udaykumar, H. S.; Mittal, R.; Rampunggoon, P.; Khanna, A. A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. (English) Zbl 1106.76428 J. Comput. Phys. 174, No. 1, 345-380 (2001). MSC: 76M25 PDFBibTeX XMLCite \textit{H. S. Udaykumar} et al., J. Comput. Phys. 174, No. 1, 345--380 (2001; Zbl 1106.76428) Full Text: DOI Link
Lai, Ming-Chih; Peskin, Charles S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. (English) Zbl 0954.76066 J. Comput. Phys. 160, No. 2, 705-719 (2000). MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{M.-C. Lai} and \textit{C. S. Peskin}, J. Comput. Phys. 160, No. 2, 705--719 (2000; Zbl 0954.76066) Full Text: DOI
Stockie, John M.; Wetton, Brian R. Analysis of stiffness in the immersed boundary method and implications for time-stepping schemes. (English) Zbl 0953.76070 J. Comput. Phys. 154, No. 1, 41-64 (1999). MSC: 76M20 76D07 74F10 PDFBibTeX XMLCite \textit{J. M. Stockie} and \textit{B. R. Wetton}, J. Comput. Phys. 154, No. 1, 41--64 (1999; Zbl 0953.76070) Full Text: DOI Link
Udaykumar, H. S.; Mittal, R.; Shyy, Wei Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids. (English) Zbl 0953.76071 J. Comput. Phys. 153, No. 2, 535-574 (1999). MSC: 76M20 76T99 80A22 76R50 PDFBibTeX XMLCite \textit{H. S. Udaykumar} et al., J. Comput. Phys. 153, No. 2, 535--574 (1999; Zbl 0953.76071) Full Text: DOI
Waldén, Johan On the approximation of singular source terms in differential equations. (English) Zbl 0938.65112 Numer. Methods Partial Differ. Equations 15, No. 4, 503-520 (1999). Reviewer: L.G.Vulkov (Russe) MSC: 65M12 65N12 35R05 35J05 35K05 PDFBibTeX XMLCite \textit{J. Waldén}, Numer. Methods Partial Differ. Equations 15, No. 4, 503--520 (1999; Zbl 0938.65112) Full Text: DOI