A high-precision discontinuous galerkin artificial viscous shock capture method based on weighted conserved variable steps

Abstract

The invention discloses a high-precision discontinuous Galerkin artificial viscous shock wave capture method based on weighted conservation variable steps. The calculation area is subdivided by unstructured grids. The control equation adopts the Euler equation, and the basis function, test function, The DG high-precision framework represented by Gauss integration points. At the same time, in the equation, a new artificial viscosity item is constructed based on the step of the conserved variable on the element interface, and the convection item of the equation is solved discretely using the HLL format, which ensures robustness and calculation accuracy under the condition of effectively capturing the shock wave; Compared with the previous method, this method only needs one empirical parameter, the actual calculation is simplified, and the step value of the conserved variable is used for calculation. Compared with the previous method, the compatibility can be guaranteed in the smooth area, and the position of the shock wave capture more accurate than previous methods.

Description

Technical field[0001]This article relates to the computational fluid dynamics technology domain, specifically to a high-precision discontinuous Galerkin artificial viscous shock capture method based on weighted conserved variable steps.Background technique[0002]Due to the excellent characteristics of high-precision calculation methods in terms of numerical dissipation and dispersion, they are more suitable for solving multi-scale flow problems such as turbulence and aerodynamic noise. Therefore, high-precision calculation methods are highly valued by more and more CFD scholars and have gained vigorous attention. development of. Among the numerous high-precision calculation methods, the high-order discontinuous Galerkin finite element (DG) method has the characteristics of strong grid adaptability, intuitive and convenient high-order scalability, and better operability of parallel algorithms. The high-order DG method has become one of the most concerned methods among many high-precis...

AI Technical Summary

Problems solved by technology

But when solving viscous equations, the smooth region does not satisfy the divergence of inviscid flux is zero, the addition of the artificial viscous term cannot guarantee the compatibility with the original equation in the smooth region

Compatibility is the basis for accurate solutions. If compatibility cannot be guaranteed, the reliability of the calculation results cannot be guaranteed, and the effect of shock wave capture will be biased.

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