A Cartesian-based embedded geometry technique with adaptive high-order finite differences for compressible flow around complex geometries

H. Uddin, R. M.J. Kramer, C. Pantano

Research output: Contribution to journalArticle

Abstract

An immersed boundary methodology to solve the compressible Navier-Stokes equations around complex geometries in Cartesian fluid dynamics solvers is described. The objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts. A standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended. Boundary conditions on the surface are enforced by an approach inspired by analytic continuation. Each fluid field is extended independently, constrained only by the boundary condition associated with that field. Unlike most existing methods, no jump conditions or explicit derivation of them from the boundary conditions are required in this approach. Numerical stiffness that arises when the fluid-solid interface is close to grid points of the mesh is addressed by preconditioning. In addition, the embedded geometry technique is coupled with a stable high-order adaptive discretization that is enabled around the object boundary to enhance resolution. The stencils used to transition the order of accuracy of the discretization are derived using the summation-by-parts technique that ensures stability. Applications to shock reflections, shock-ramp interactions, and supersonic and low-Mach number flows over two- and three-dimensional geometries are presented.

Original languageEnglish (US)
Pages (from-to)379-407
Number of pages29
JournalJournal of Computational Physics
Volume262
DOIs
StatePublished - Apr 1 2014

Keywords

  • Compressible Navier-Stokes
  • Embedded geometry
  • High-order finite differences
  • Immersed boundary
  • Immersed interface

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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