Nessyahu–Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids Original Research Article

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. The modification avoids the intermediate predictor time step between tn and tn+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.