Second-order-accurate explicit fluctuation splitting schemes for unsteady problems

This paper is concerned with the issue of obtaining explicit fluctuation splitting schemes which achieve second-order accuracy in both space and time on an arbitrary unstructured triangular mesh. A theoretical analysis demonstrates that, for a linear reconstruction of the solution, mass lumping does not diminish the accuracy of the scheme provided that a Galerkin space discretization is employed. Thus, two explicit fluctuation splitting schemes are devised which are second-order accurate in both space and time, namely, the well known Lax-Wendroff scheme and a Lax-Wendroff-type scheme using a three-point-backward discretization of the time derivative. A thorough mesh-refinement study verifies the theoretical order of accuracy of the two schemes on meshes with increasing levels of nonuniformity.