A central compact hybrid-variable method with spectral-like resolution: One-dimensional case

Abstract

We present a central compact hybrid-variable method (CHVM) with spectral-like accuracy for first-order hyperbolic problems with moderate or less discontinuities. It incorporates the compact difference strategy and a recently proposed hybrid-variable discretization technique to achieve even higher accuracy on a given stencil of grid cells. The CHVM is first constructed for the one-dimensional (1D) model linear advection equations, in which case the accuracy and stability analysis are conducted; then it is extended to 1D nonlinear problems such as the Burgers’ equation and the Euler equations. A novel Gauss–Seidel type low-pass high-order filter is constructed to suppress spurious oscillations near discontinuities. The performance of the proposed method is assessed by extensive benchmark tests.