Abstract
By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.
Highlights
In computational fluid dynamics (CFD), numerical schemes greatly influence the computational accuracy, efficiency, and robustness
The CPR methods are equivalent to specific discontinuous Galerkin (DG) methods, while their calculation cost is relatively lower because they are based on a differential formulation and avoid expensive integration calculations [8]
A way around this problem is to develop a hybrid scheme of high-order finite element methods (CPR or DG) and finite difference (FD) or finite volume (FV) methods, which provide better shock-capturing abilities locally near shocks
Summary
In computational fluid dynamics (CFD), numerical schemes greatly influence the computational accuracy, efficiency, and robustness. A way around this problem is to develop a hybrid scheme of high-order finite element methods (CPR or DG) and finite difference (FD) or finite volume (FV) methods, which provide better shock-capturing abilities locally near shocks. In this way, high-order finite element methods are adopted in smooth regions, which maintain compactness and high resolution. Cheng et al developed multidomain hybrid RKDG and WENO methods [20, 21] with good geometry flexibility and low computational costs These methods show good shock-capturing ability because they avoid using high-order finite element methods to capture shocks directly, but utilize schemes with better shockcapturing abilities instead.
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