Finite Volumes for Complex Applications II by Fayssal Benkhaldoun, Roland Vilsmeier

By Fayssal Benkhaldoun, Roland Vilsmeier

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For the Euler equations, the flux jacobians A^ have one common eigenvector so that it is possible to decouple one scalar equation from the original system, leaving a coupled 3x3 system and one decoupled scalar equation in 2D. The transformation to symmetrizing variables defined as dQ = (-^,du,dp a2dp}1 accomplishes this task. The decoupled scalar equation is nothing else than the entropy advection equation, which is well-known to derive from the Euler equations. As shown in [PAI 97], additional decoupling may be achieved by preconditioning, namely the system of equations is rewritten as1 and the residual distribution method is applied to the preconditioned system between brackets.

Characteristic time stepping or local preconditioning of the Euler equations. AIAA Paper 91-1552-CP. [WAT 97] N. P. Waterson and H. Deconinck. A fully-implicit multidimensional upwind approach for the incompressible Navier-Stokes equations. In C. Taylor, editor, Numerical methods in laminar and turbulent flows, volume X. Pineridge Press, 1997. Overcoming mass losses in Level Set-based interface tracking schemes Th. Schneider and R. Klein Konrad-Zuse-Zentrum fur Informationstechnik Berlin, Germany FB Mathematik & Informatik, Freie Universitdt Berlin, Germany ABSTRACT An extended level set method is presented for tracking material interfaces in incompressible two-phase flow that ensures conservation of mass.

1987. [vdW 99] E. van der Weide, H. Deconinck, E. Issman, and G. Degrez. A parallel, implicit, multidimensional upwind residual distribution method for the Navier-Stokes equations on unstructured grids. Computational Mechanics, 23(2): 199-208, 1999. [vLE 91] B. van Leer, W. T. Lee, and P. L. Roe. Characteristic time stepping or local preconditioning of the Euler equations. AIAA Paper 91-1552-CP. [WAT 97] N. P. Waterson and H. Deconinck. A fully-implicit multidimensional upwind approach for the incompressible Navier-Stokes equations.

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