Pareschi, Lorenzo; Rey, Thomas Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation. (English) Zbl 1511.76073 SIAM J. Numer. Anal. 60, No. 6, 3216-3240 (2022). MSC: 76M22 76P05 PDFBibTeX XMLCite \textit{L. Pareschi} and \textit{T. Rey}, SIAM J. Numer. Anal. 60, No. 6, 3216--3240 (2022; Zbl 1511.76073) Full Text: DOI arXiv
Alekseenko, Alexander; Martin, Robert; Wood, Aihua Fast evaluation of the Boltzmann collision operator using data driven reduced order models. (English) Zbl 07599591 J. Comput. Phys. 470, Article ID 111526, 14 p. (2022). MSC: 76Pxx 82Cxx 65Mxx PDFBibTeX XMLCite \textit{A. Alekseenko} et al., J. Comput. Phys. 470, Article ID 111526, 14 p. (2022; Zbl 07599591) Full Text: DOI
Hu, Jingwei; Huang, Xiaodong; Shen, Jie; Yang, Haizhao A fast Petrov-Galerkin spectral method for the multidimensional Boltzmann equation using mapped Chebyshev functions. (English) Zbl 1490.35247 SIAM J. Sci. Comput. 44, No. 3, A1497-A1524 (2022). MSC: 35Q20 65M70 PDFBibTeX XMLCite \textit{J. Hu} et al., SIAM J. Sci. Comput. 44, No. 3, A1497--A1524 (2022; Zbl 1490.35247) Full Text: DOI arXiv
Boscheri, Walter; Dimarco, Giacomo High order modal discontinuous Galerkin implicit-explicit Runge Kutta and linear multistep schemes for the Boltzmann model on general polygonal meshes. (English) Zbl 1521.76319 Comput. Fluids 233, Article ID 105224, 21 p. (2022). MSC: 76M10 65M60 65L06 76P05 76X05 PDFBibTeX XMLCite \textit{W. Boscheri} and \textit{G. Dimarco}, Comput. Fluids 233, Article ID 105224, 21 p. (2022; Zbl 1521.76319) Full Text: DOI arXiv
Boscheri, Walter; Dimarco, Giacomo High order finite volume schemes with IMEX time stepping for the Boltzmann model on unstructured meshes. (English) Zbl 1507.65147 Comput. Methods Appl. Mech. Eng. 387, Article ID 114180, 33 p. (2021). MSC: 65M08 PDFBibTeX XMLCite \textit{W. Boscheri} and \textit{G. Dimarco}, Comput. Methods Appl. Mech. Eng. 387, Article ID 114180, 33 p. (2021; Zbl 1507.65147) Full Text: DOI arXiv
Jaiswal, Shashank Isogeometric schemes in rarefied gas dynamics context. (English) Zbl 1506.76155 Comput. Methods Appl. Mech. Eng. 383, Article ID 113926, 47 p. (2021). MSC: 76P05 35Q20 65D07 76M10 65M60 65T50 65Y05 82C40 82D05 PDFBibTeX XMLCite \textit{S. Jaiswal}, Comput. Methods Appl. Mech. Eng. 383, Article ID 113926, 47 p. (2021; Zbl 1506.76155) Full Text: DOI
Zweck, John; Chen, Yanping; Goeckner, Matthew J.; Shen, Yannan Spectral computation of low probability tails for the homogeneous Boltzmann equation. (English) Zbl 1475.65151 Appl. Numer. Math. 162, 301-317 (2021). Reviewer: Hendrik Ranocha (Münster) MSC: 65M70 35Q20 65M06 65L06 65M15 82C70 82C40 82D10 PDFBibTeX XMLCite \textit{J. Zweck} et al., Appl. Numer. Math. 162, 301--317 (2021; Zbl 1475.65151) Full Text: DOI arXiv
Yao, Zheng-an; Zhou, Yu-Long High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials. (English) Zbl 1442.35291 Kinet. Relat. Models 13, No. 3, 435-478 (2020). MSC: 35Q20 35R11 76P05 PDFBibTeX XMLCite \textit{Z.-a. Yao} and \textit{Y.-L. Zhou}, Kinet. Relat. Models 13, No. 3, 435--478 (2020; Zbl 1442.35291) Full Text: DOI
Narski, Jacek Fast kinetic scheme: efficient MPI parallelization strategy for 3D Boltzmann equation. (English) Zbl 1474.76057 Commun. Comput. Phys. 25, No. 2, 361-389 (2019). MSC: 76M28 65Y05 65M70 76P05 PDFBibTeX XMLCite \textit{J. Narski}, Commun. Comput. Phys. 25, No. 2, 361--389 (2019; Zbl 1474.76057) Full Text: DOI arXiv
Keßler, Torsten; Rjasanow, Sergej Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation. (English) Zbl 1421.82032 Kinet. Relat. Models 12, No. 3, 507-549 (2019). MSC: 82C80 82C40 65N35 33C45 35L04 65M08 PDFBibTeX XMLCite \textit{T. Keßler} and \textit{S. Rjasanow}, Kinet. Relat. Models 12, No. 3, 507--549 (2019; Zbl 1421.82032) Full Text: DOI
Kitzler, Gerhard; Schöberl, Joachim A polynomial spectral method for the spatially homogeneous Boltzmann equation. (English) Zbl 1421.35238 SIAM J. Sci. Comput. 41, No. 1, B27-B49 (2019). Reviewer: Mária Lukáčová (Mainz) MSC: 35Q20 65M70 65M60 76P05 82C40 PDFBibTeX XMLCite \textit{G. Kitzler} and \textit{J. Schöberl}, SIAM J. Sci. Comput. 41, No. 1, B27--B49 (2019; Zbl 1421.35238) Full Text: DOI arXiv
Gamba, Irene M.; Rjasanow, Sergej Galerkin-Petrov approach for the Boltzmann equation. (English) Zbl 1406.65094 J. Comput. Phys. 366, 341-365 (2018). MSC: 65M70 35Q20 76P05 PDFBibTeX XMLCite \textit{I. M. Gamba} and \textit{S. Rjasanow}, J. Comput. Phys. 366, 341--365 (2018; Zbl 1406.65094) Full Text: DOI arXiv
Alekseenko, Alexander; Nguyen, Truong; Wood, Aihua A deterministic-stochastic method for computing the Boltzmann collision integral in \(\mathcal{O}(MN)\) operations. (English) Zbl 1405.76040 Kinet. Relat. Models 11, No. 5, 1211-1234 (2018). MSC: 76P05 76M10 65M60 PDFBibTeX XMLCite \textit{A. Alekseenko} et al., Kinet. Relat. Models 11, No. 5, 1211--1234 (2018; Zbl 1405.76040) Full Text: DOI
Alonso, Ricardo J.; Gamba, Irene M.; Tharkabhushanam, Sri Harsha Convergence and error estimates for the Lagrangian-based conservative spectral method for Boltzmann equations. (English) Zbl 1404.76185 SIAM J. Numer. Anal. 56, No. 6, 3534-3579 (2018). MSC: 76M22 65M70 35A22 35Q20 45K05 65M12 76P05 PDFBibTeX XMLCite \textit{R. J. Alonso} et al., SIAM J. Numer. Anal. 56, No. 6, 3534--3579 (2018; Zbl 1404.76185) Full Text: DOI arXiv
Zhang, Chenglong; Gamba, Irene M. A conservative discontinuous Galerkin solver for the space homogeneous Boltzmann equation for binary interactions. (English) Zbl 1403.65079 SIAM J. Numer. Anal. 56, No. 5, 3040-3070 (2018). MSC: 65M60 65Y05 45K05 82B40 65M15 65F50 35Q20 PDFBibTeX XMLCite \textit{C. Zhang} and \textit{I. M. Gamba}, SIAM J. Numer. Anal. 56, No. 5, 3040--3070 (2018; Zbl 1403.65079) Full Text: DOI
Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas An efficient numerical method for solving the Boltzmann equation in multidimensions. (English) Zbl 1380.76088 J. Comput. Phys. 353, 46-81 (2018). MSC: 76M22 76P05 35Q20 65M70 PDFBibTeX XMLCite \textit{G. Dimarco} et al., J. Comput. Phys. 353, 46--81 (2018; Zbl 1380.76088) Full Text: DOI arXiv
Abdelmalik, M. R. A.; van Brummelen, E. H. Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation. (English) Zbl 1439.76144 Comput. Methods Appl. Mech. Eng. 325, 219-239 (2017). MSC: 76P05 65N30 35A35 35Q20 76M10 PDFBibTeX XMLCite \textit{M. R. A. Abdelmalik} and \textit{E. H. van Brummelen}, Comput. Methods Appl. Mech. Eng. 325, 219--239 (2017; Zbl 1439.76144) Full Text: DOI arXiv
Gamba, Irene M.; Haack, Jeffrey R.; Hauck, Cory D.; Hu, Jingwei A fast spectral method for the Boltzmann collision operator with general collision kernels. (English) Zbl 1394.35310 SIAM J. Sci. Comput. 39, No. 4, B658-B674 (2017). Reviewer: Catalin Popa (Iaşi) MSC: 35Q20 65M70 65T50 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., SIAM J. Sci. Comput. 39, No. 4, B658--B674 (2017; Zbl 1394.35310) Full Text: DOI arXiv
Peng, Ao-Ping; Li, Zhi-Hui; Wu, Jun-Lin; Jiang, Xin-Yu Implicit gas-kinetic unified algorithm based on multi-block docking grid for multi-body reentry flows covering all flow regimes. (English) Zbl 1373.76073 J. Comput. Phys. 327, 919-942 (2016). MSC: 76G25 76M12 PDFBibTeX XMLCite \textit{A.-P. Peng} et al., J. Comput. Phys. 327, 919--942 (2016; Zbl 1373.76073) Full Text: DOI
Alekseenko, Alexander; Euler, Craig A Bhatnagar-Gross-Krook kinetic model with velocity-dependent collision frequency and corrected relaxation of moments. (English) Zbl 1365.82017 Contin. Mech. Thermodyn. 28, No. 3, 751-763 (2016). MSC: 82C40 76P05 PDFBibTeX XMLCite \textit{A. Alekseenko} and \textit{C. Euler}, Contin. Mech. Thermodyn. 28, No. 3, 751--763 (2016; Zbl 1365.82017) Full Text: DOI
Hu, Jingwei; Jin, Shi A stochastic Galerkin method for the Boltzmann equation with uncertainty. (English) Zbl 1349.82088 J. Comput. Phys. 315, 150-168 (2016). MSC: 82C80 65M75 45K05 82C40 PDFBibTeX XMLCite \textit{J. Hu} and \textit{S. Jin}, J. Comput. Phys. 315, 150--168 (2016; Zbl 1349.82088) Full Text: DOI
Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien Spectral method for a kinetic swarming model. (English) Zbl 1349.76682 J. Comput. Phys. 297, 32-46 (2015). MSC: 76M28 78M12 65M70 76P05 82C22 PDFBibTeX XMLCite \textit{I. M. Gamba} et al., J. Comput. Phys. 297, 32--46 (2015; Zbl 1349.76682) Full Text: DOI
Dimarco, G.; Pareschi, L. Numerical methods for kinetic equations. (English) Zbl 1398.65260 Acta Numerica 23, 369-520 (2014). MSC: 65M75 76P05 82D10 PDFBibTeX XMLCite \textit{G. Dimarco} and \textit{L. Pareschi}, Acta Numerica 23, 369--520 (2014; Zbl 1398.65260) Full Text: DOI
Alekseenko, A.; Josyula, E. Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space. (English) Zbl 1349.82051 J. Comput. Phys. 272, 170-188 (2014). MSC: 82C40 82C80 65M60 PDFBibTeX XMLCite \textit{A. Alekseenko} and \textit{E. Josyula}, J. Comput. Phys. 272, 170--188 (2014; Zbl 1349.82051) Full Text: DOI arXiv
Gamba, Irene M.; Haack, Jeffrey R. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit. (English) Zbl 1349.82080 J. Comput. Phys. 270, 40-57 (2014). MSC: 82C80 76M22 65M70 76P05 82C31 82D10 PDFBibTeX XMLCite \textit{I. M. Gamba} and \textit{J. R. Haack}, J. Comput. Phys. 270, 40--57 (2014; Zbl 1349.82080) Full Text: DOI arXiv
Munafò, Alessandro; Haack, Jeffrey R.; Gamba, Irene M.; Magin, Thierry E. A spectral-Lagrangian Boltzmann solver for a multi-energy level gas. (English) Zbl 1349.76720 J. Comput. Phys. 264, 152-176 (2014). MSC: 76M28 65M75 76P05 82C80 82C40 PDFBibTeX XMLCite \textit{A. Munafò} et al., J. Comput. Phys. 264, 152--176 (2014; Zbl 1349.76720) Full Text: DOI arXiv
Filbet, Francis; Rey, Thomas A rescaling velocity method for dissipative kinetic equations. Applications to granular media. (English) Zbl 1349.76330 J. Comput. Phys. 248, 177-199 (2013). MSC: 76M12 76M22 65M08 65M70 65M75 76T25 82C40 PDFBibTeX XMLCite \textit{F. Filbet} and \textit{T. Rey}, J. Comput. Phys. 248, 177--199 (2013; Zbl 1349.76330) Full Text: DOI arXiv
Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao Deterministic numerical solutions of the Boltzmann equation using the fast spectral method. (English) Zbl 1349.76790 J. Comput. Phys. 250, 27-52 (2013). MSC: 76P05 65M70 PDFBibTeX XMLCite \textit{L. Wu} et al., J. Comput. Phys. 250, 27--52 (2013; Zbl 1349.76790) Full Text: DOI Link