Large time step wave adding scheme for systems of hyperbolic conservation laws

The current paper presents a large time step wave adding scheme (hereafter LTS-WA) originated in LeVeque's large time Godunov scheme, i.e. constructing numerical schemes via adding strong waves of discontinuity decomposition. Compared with the original scheme, we use a different strategy for wave adding and extend it to multi-dimensional cases. For rarefaction waves, we propose a grid cell decomposition method which can automatically satisfy the entropy condition and avoid nonphysical solutions. We give detailed formulae of the scheme, and make numerical experiments using scalar equations and Euler equations in one and multi-dimensional cases. Numerical results show that, besides the advantage of large time step, the new scheme has a lower numerical dissipation and a higher resolution of shocks and contact discontinuities with the increase of CFL number in certain range.