An Algorithm for Euler Equations Using Adaptive Unstructured Grid Based on Riemann Problem Solution

An algorithm to solve two dimensional Euler equations on adaptive unstructured grids is presented.It uses the analytical solution of Riemann problem to calculate the numerical conservative fluxes.With the velocity tangent to the face being treated as a passively advected quantity, the flux is obtained by solving Riemann problem for the projected equations along the normal to that face.Within the framework of adaptive mesh refinement,the algorithm obtains high resolution.Convergence to steady state is accelerated by multigrid method.Cases are run for subsonic and supersonic internal flows.The results show that the algorithm is robust and accurate,even in the presence of nonlinear discontinuities.