TITLE:

ADVANCE HYBRID HIGH ORDER METHODS FOR MULTI-SCALES PROBLEMS IN SHOCKED FLOWS

DATE:

Friday, March 21st, 2008

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Wai Sun Don, visiting Professor, Division of Applied Mathematics, Brown University

ABSTRACT:

Classical high order methods such as spectral methods and classical WENO methods are reaching their limits in handling shocked flows with both large and small scales structures, such as the classical Richtmyer-Meshkov instability and shock-particle laden flow, in an efficient and accurate manner due to some of their inherent weakness. Spectral methods, though highly efficient and accuracy for smooth problems, suffer the Gibbs oscillations when discontinuities formed in the solution in a nonlinear hyperbolic conservation laws. High order WENO methods, on the other hand, are capable of capturing shocks in an essentially non-oscillatory manner due to its non-linear adaptive stencils switching and lowering of the order at the non-smooth stencils. However, the reconstruction procedure is an expensive undertaking and quite dissipative in nature. In this talk, I will present the work on the hybridization of these two methodologically different methods in a spatially and temporary adaptive multi-domain framework yielding a scheme which can capture shock and resolving smooth small scales structures in an efficient manner. The adaptively is based on the high order multi-resolution analysis. Examples of the standard Riemann IVP problems, Mach 3 shock-density wave interaction and two dimensional Shock-vortex interaction and Richtmyer-Meshkov instability at high Mach numbers will be shown.

HOST:

Guus Jacobs

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