Application of a third-order reconstruction scheme to hypersonic reacting flows using unstructured meshes and multigrid techniques

In this paper a high-order finite-volume method is studied to solve hypersonic steady chemically reacting flows on unstructured meshes. The quadratic polynomial reconstruction scheme is first presented as well as the monotonicity enforcement technique used to limit the oscillations in the vicinity of shock waves and regions with high gradients. The implicit time-integration procedure is based on Newton linearization and uses the GMRES algorithm. The preconditioning of the linear systems, based on an iterative inversion of a low-order Jacobian, coupled with a multigrid technique, is also discussed. Results obtained for the test case corresponding to the hypersonic flow around a double ellipse are presented.