TITLE:

Development and study of high order WENO-Z Finite difference scheme for nonlinear hyperbolic PDEs

DATE:

Friday, Feb 8th, 2013

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Wai Sun Don.
Computational Science Research Center.
San Diego State University.

ABSTRACT:

In this talk, I will discuss the development of the high order WENO-Z fnite difference scheme for
solving nonlinear hyperbolic system of conservation laws. The WENO-Z scheme has the property
that it is less dissipative and has better resolution for high frequency waves (efficient), than say, the
classical WENO-JS scheme. In the reconstruction step of fifth order WENO schemes for solving
hyperbolic conservation laws, nonlinear weights ωk are designed to recover the formal fifth order
(optimal order) of the upwinded central finite difference scheme when the solution is sufficiently
smooth. However, it has been demonstrated that, in the present of critical points (functions with
zero first and second derivatives, for example), the order of accuracy is less than optimal. We
will analyze the nonlinear weights and prove that the optimal order can be restored if the free
parameters ε used in the local smoothness indicators βk is defined as ε = Ω(Δxm ), even in the
present of the critical points of any order, for WENO-JS (m = 2) and WENO-Z scheme (m ‚â• 2).
Both theoretical results are con?rmed numerically on smooth functions with arbitrary order of
critical points. This is a highly desirable feature, as illustrated with the Lax problem and the Mach
3 shock-density wave interaction of one dimensional Euler equations, for a smaller ε allows a better
essentially non-oscillatory shock capturing as it does not over-dominate over the size of βk . If time
allows, some recent work on the development of a fifth order WENO-Z PSIC method, where the
fluid is solved in the Eulerian framework while the particles is tracked in the Lagrangian framework,
for simulating shock-particles laden flows will also presented.

HOST:

Dr. Guus Jacobs.

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