A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
2007 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 225, no 1, 1020-1038 p.Article in journal (Refereed) Published
We construct a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate. The equations are discretized with high-order accurate finite difference methods that satisfy a Summation-By-Parts rule. The boundary conditions are imposed with penalty terms known as the Simultaneous Approximation Term technique. The main result is a stability proof for the full three-dimensional Navier-Stokes equations, including the boundary conditions. We show the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known. We demonstrate the stability and discuss the non-reflecting properties of the outflow conditions for a vortex in free space. Furthermore, we compute the three-dimensional vortex shedding behind a circular cylinder in an oblique free stream for Mach number 0.5 and Reynolds number 500.
Place, publisher, year, edition, pages
2007. Vol. 225, no 1, 1020-1038 p.
high-order finite difference methods, boundary conditions, compressible Navier-Stokes equations, stability, accuracy, wellposedness, summation-by-parts, simultaneous approximation terms
IdentifiersURN: urn:nbn:se:kth:diva-16883DOI: 10.1016/j.jcp.2007.01.023ISI: 000248854300051ScopusID: 2-s2.0-34447250344OAI: oai:DiVA.org:kth-16883DiVA: diva2:334926
QC 201005252010-08-052010-08-05Bibliographically approved