A High-Precision Discontinuous Galerkin Artificial Viscous Shock Capture Method Based on Flow Field Density Step

Abstract

The invention discloses a high-precision discontinuous Galerkin artificial viscous shock wave capture method based on the flow field density step. By establishing a DG high-precision frame, the control equation adopts the Euler equation, and the calculation area is divided by an unstructured grid. The convection term of the equation is solved discretely using the high-order HLLC scheme. At the same time, an artificial viscosity term is added on the basis of the master control equation to capture the shock wave on the basis of ensuring robustness and calculation accuracy. The addition of the artificial viscosity term is based on the grid unit surface The step above does not require the shock wave detection technology, and the normalization method is used to ensure that the dimensions are consistent and the step quantity is assigned to the grid unit; the present invention selects the density as the step variable to construct the artificial viscosity, and does not require additional In the process of shock wave detection and other processes, the construction algorithm requires fewer variables and the calculation process is simplified. Compared with the previous shock wave capture method, the shock wave capture efficiency of this method is improved, and the number of iteration steps required to effectively capture the shock wave Significantly less CPU time used.

Description

technical field [0001] This paper relates to computational fluid dynamics technology, specifically a high-precision discontinuous Galerkin artificial viscous shock capture method. Background technique [0002] Due to the excellent characteristics of the high-precision discontinuous Galerkin (DG) method in numerical dissipation and dispersion, it has been highly valued by more and more CFD scholars and has been developed vigorously. According to Godunov's principle, no linear scheme with higher than first-order precision will have a single mediation. The high-precision DG method will produce Gibbs phenomenon near the shock discontinuity, which will cause the generation of non-physical understanding and lead to the interruption of calculation. How to effectively capture the shock wave and ensure the monotonicity and robustness of the format has become one of the important development directions of the DG method. In the DG method, there are generally limiter and reconstructio...

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Problems solved by technology

[0005] The purpose of the present invention is to propose a high-precision discontinuous Galerkin artificial viscous shock wave capture method based on the flow field density step. This method needs to carry out shock wave detection in advance in the previous high-precision DG format shock wave capture, and the process is complicated. etc., based on the characteristics of the physical understanding in the flow field, under the condition of ensuring the same dimension and ensuring the robustness and stability, the shock wave detection process is omitted, and the structure required for shock wave capture is simplified variable

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