Weighted conserved variable step-based high-precision discontinuous Galerkin artificial viscosity shock wave capturing method

Abstract

The invention discloses a weighted conserved variable step-based high-precision discontinuous Galerkin artificial viscosity shock wave capturing method. according to the method, an unstructured grid is adopted to subdivide a calculation area; an Euler equation is adopted as a control equation; a DG high-precision framework which takes a primary function, a test function and a Gauss integral pointas representatives is established; on the equation, a new artificial conserved variable step-based high-precision discontinuous Galerkin artificial viscosity term is constructed by taking a step of conserved variable on a unit interface; and a convective term of the equation is discretely solved by adoption of an HLL format, so that the robustness and calculation precision are ensured under the condition of effectively capturing shock waves. Compared with past methods, the method only needs one experience parameter, so that the practical calculation is simplified; step amounts of conversed variables are adopted to carry out calculation; and compared with past methods, the method is capable of ensuring compatibility in smooth areas, so that the shock wave capturing positions are more correct than that of the past methods.

Description

technical field [0001] This paper relates to computational fluid dynamics technology domain, specifically to a high-precision discontinuous Galerkin artificial viscous shock capture method based on weighted conservation 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 turbulent flow and aerodynamic noise. develop. Among the large number of high-precision calculation methods, the high-order discontinuous Galerkin finite element (DG) method has the characteristics of strong mesh adaptability, intuitive and convenient high-order scalability, and good parallel algorithm operability. The high-order DG method has become one of the most concerned methods among many high-precision computing methods. According to the Godunov principle, the high-precision DG method will produce the Gibbs phenome...

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.

Images