The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws

This paper presents a finite volume local evolution Galerkin (FVLEG) scheme for solving the hyperbolic conservation laws. The FVLEG scheme is the simplification of the finite volume evolution Galerkin method (FVEG). In FVEG, a necessary step is to compute the dependent variables at cell interfaces at tn + τ (0 < τ ⩽ Δt). The FVLEG scheme is constructed by taking τ → 0 in the evolution operators of FVEG. The FVLEG scheme greatly simplifies the evaluation of the numerical fluxes. It is also well suited with the semi-discrete finite volume method, making the flux evaluation being decoupled with the reconstruction procedure while maintaining the genuine multi-dimensional nature of the FVEG methods. The derivation of the FVLEG scheme is presented in detail. The performance of the proposed scheme is studied by solving several test cases. It is shown that FVLEG scheme can obtain very satisfactory numerical results in terms of accuracy and resolution.