A central compact hybrid-variable method with spectral-like resolution: one-dimensional case. (English) Zbl 1498.65135
Summary: 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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |
Keywords:
hybrid-variable methods; compact scheme; spectral-like accuracy; hyperbolic equations; unconditional stability; low-pass filter for hybrid dataReferences:
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