Transversal effects of high order numerical schemes for compressible fluid flows
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Finite volume schemes for the two-dimensional (2D) wave system are taken to demonstrate the role of the genuine dimensionality of Lax-Wendroff flow solvers for compressible fluid flows. When the finite volume schemes are applied, the transversal variation relative to the computational cell interfaces is neglected, and only the normal numerical flux is used, thanks to the Gauss-Green formula. In order to offset such defects, the Lax-Wendroff flow solvers or the generalized Riemann problem (GRP) solvers are adopted by substituting the time evolution of flows into the spatial variation. The numerical results show that even with the same convergence rate, the error by the GRP2D solver is almost one ninth of that by the multistage Runge-Kutta (RK) method.
Key wordstransversal effect generalized Riemann problem (GRP) solver Lax-Wendroff flow solver wave system
Chinese Library ClassificationO357.4
2010 Mathematics Subject Classification76D17 76E09
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