Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

✍ Scribed by I. Lomtev; C.B. Quillen; G.E. Karniadakis

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 920 KB
• Volume: 144
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5831

✦ Synopsis

In this paper we describe the foundation of a spectral/hp method suitable for simulating viscous compressible flows with shocks on standard unstructured meshes. It is based on a discontinuous Galerkin formulation for the hyperbolic contributions combined with a mixed Galerkin formulation for the diffusive contributions. Highorder accuracy is achieved by using a recently developed hierarchical spectral basis. This basis is formed by combining Jacobi polynomials of high-order weights written in a new coordinate system that retains a tensor product property and accurate numerical quadrature. The formulation is conservative, and monotonicity is enforced by high-order limiters and by appropriately lowering the basis order around discontinuities. Convergence results are shown for benchmark solutions of the advection, Euler, and Navier-Stokes equations that demonstrate exponential convergence of the new method. Flow simulations for subsonic and supersonic flows are also presented that demonstrate discretization flexibility using hp type refinement. Unlike other high-order methods the new method uses standard finite volume meshes consisting of arbitrary triangulizations.