An approximate Lax-Wendroff-type procedure for high order accurate schemes for hyperbolic conservation laws
The PDEs considered in this work are systems of \(m\) \(d\)-dimensional hyperbolic conservation laws \(u_t+\nabla\cdot f(u)=0\), where \(\nabla\cdot\) denotes the divergence operator with respect to the spatial variables \(x=(x_1,\dots,x_d)\) and \(u=u(x,t)\in \mathbb R^m\). A high-order time stepping applied to spatial discretizations provided by the method of lines is presented. The authors focus on developing a version which, instead of computing the exact expressions of the time derivatives of the fluxes, approximates them through high-order central divided difference formulas. This paper is organized as follows. The first section is the Introduction. In Section 2, the details about the general framework and a general overview of the exact Lax-Wendroff type procedure is shown. Section 3 stands for the formulation of the approximate Lax-Wendroff-type procedure, where some important properties, such as the achievement of the desired accuracy order and the conservation form, are proven. Several numerical experiments comparing both techniques are presented in Section 4 and some conclusions are drawn in Section 5.
scientific article; zbMATH DE number 6849356