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Chongam Kim

2013-11-11
14:10:00 - 15:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

This tutorial surveys various limiting strategies to solve compressible flows. Starting from the basic concept of non-linear stability for hyperbolic conservation laws, it reviews some remarkable progresses of limiting methods, such as TVD-MUSCL and ENO/WENO. While these approaches may work successfully in many cases, it is often insufficient or almost impossible to control oscillations near shock discontinuity in multi-dimensional situations. In order to find out a suitable criterion for oscillation-control in multiple dimensions, the one-dimensional monotonic condition is extended to multi-dimensional space, and multi-dimensional limiting process (MLP) is formulated on structured grids. By examining its design principle and implementation on structured grids in detail, we explore remarkably enhanced accuracy and convergence characteristics to compute multi-dimensional compressible flows.

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