High Order Numerical Simulation Of Flow Field Based On Interior Penalty DG Chimera Grid

Chimera grid technology has been applied to various engineering fields since it was proposed.Chimera grid is a very effective tool for meshing complex shapes and relative motion systems.Various numerical methods and mature boundary conditions can still be applied in chimera grids.With the vigorous development of numerical methods in recent years,high-precision numerical methods have attracted more and more attention because of their small numerical dissipation and dispersion.They have outstanding advantages in solving multi-scale flow problems.The application of highprecision numerical methods in chimera grid has also become a new trend.Among many high-precision algorithms,Discontinuous Galerkin(DG)method has attracted much attention because of its high calculation accuracy,good compactness and good mathematical characteristics.In this paper,the compressible Navier Stokes(N-S)equation is solved by using the Interior Penalty Discontinuous Galerkin(IPDG)method in chimera grid.Taking the viscous flux as an auxiliary variable,the N-S equation is decomposed into two firstorder equations,and then the spatial term of the equation is discretized by DG method to obtain the spatial semi discrete equation,and the Newton Krylov implicit method is used for time advance.For the case of strong discontinuities in the flow field,the stability of the calculation is improved by adding an artificial viscosity term,and the hgrid adaptive technology is applied to improve the shock resolution.The Hole-Map method is used to "hole cutting" in chimera grid,constructing the hole boundary.The contribution element of Gaussian integral point is located by using template roaming method and KD-Tree search algorithm,and then realize the flow field information interaction in different calculation domains through the interpolation process.Firstly,the accuracy of the method is verified by isentropic vortex problem and couetee flow.On this basis,the numerical simulation of inviscid two-dimensional transonic and three-dimensional subsonic NACA0012 airfoils is carried out to further verify the robustness and reliability of the method in the inviscid case.For the viscous case,the robustness and reliability of the method is verified by typical examples of steady and unsteady cylindrical flow,subsonic and supersonic NACA0012 airfoil flow and three-dimensional spherical flow.In the transonic and supersonic examples,the artificial viscosity is added to suppress the nonphysical oscillation and improve the stability of the calculation.At the same time,the h-grid adaptive technology is applied to improve the shock resolution.The numerical results show the effectiveness of the method.