A high-precision discontinuous galerkin artificial viscous shock capture method

Abstract

The invention discloses a high-precision discontinuous Galerkin artificial viscous shock wave capture method based on the flow field flux step. The calculation area is subdivided by unstructured grids. The control equation adopts Euler equation, and the basis function and test function are established. , Gauss integration point as the representative of the DG high-precision framework, and at the same time, a new artificial viscosity term is constructed based on the step of the conserved variable on the element interface in the equation. In the case of , the robustness and calculation accuracy are guaranteed; even if the present invention does not capture the shock wave, the flux at the element interface is also a necessary intermediate variable for solving the equation, and the flux at the interface of the flow field element is selected Steps are used to construct artificial stickiness, which can reduce the amount of calculation compared with other methods, thereby saving calculation time.

Description

technical field [0001] This paper relates to computational fluid dynamics technology flow field, specifically a high-precision discontinuous Galerkin artificial viscous shock capture method based on flow field flux steps. Background technique [0002] The high-precision DG method currently has excellent characteristics in numerical dissipation and dispersion, and is theoretically very suitable for solving complex multi-scale problems in fluid calculations. The high-precision DG method has achieved certain results in the calculation of low-speed incompressible fluids and obtained widely used. However, when the high-precision DG method is applied to the calculation of compressible fluid, shock waves will be generated in the flow field. According to the Godunov principle, the high-precision DG method will produce Gibbs phenomenon near the shock wave discontinuity, which will cause the generation of non-physical understanding and lead to calculation interruption. Shock wave ca...

AI Technical Summary

Problems solved by technology

[0003] The purpose of the present invention is to propose a high-precision discontinuous Galerkin artificial viscous shock wave capture method. According to the characteristics of the shock wave and the principle of dimension analysis, the method adopts the flux step on the unit interface in the flow field to construct a new The artificial viscous shock wave capture method is mainly used to solve the problems of poor convergence, poor robustness, prone to non-physical vibration, and insufficient shock wave capture encountered in the high-precision DG method during the shock wave capture process.

Images