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Nessyahu-Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids. (English) Zbl 1025.65048
Summary: A new modified version of the Nessyahu-Tadmor (NT) 1-dimensional finite volume central scheme is presented, as well as corresponding new versions for 2D-structured and 3D-unstructured grids inspired from the NT-scheme [cf. H. Nessyahu and E. Tadmor, J. Comput. Phys. 87, 408-463 (1990; Zbl 0697.65068)]. The modification avoids the intermediate predictor time step between t\(^{n}\) and t\(^{n+1}\). Although this does not really bring about substantial accuracy/computer time improvements in the 1D case, in the 2- and 3-dimensional cases, the modified scheme does lead to important reductions in computer times. 3D comparative simulations for the shock tube problem and for a supersonic inviscid flow through a channel with a 4\(\%\) circular bump are presented.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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