High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems
Final rept. 25 Sep 2008 - 24 Sep 2012
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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We have performed research on the design of new algorithms and improvement of existing algorithms for high order accurate finite difference and finite volume weighted essentially non-oscillatory WENO schemes and discontinuous Galerkin finite element methods, for solving partial differential equations with discontinuous, rapidly changing, or multiscale solutions. Applications to computational fluid dynamics, astrophysical problems, and pedestrian flows are addressed. The objective of improving the range of applicability, efficiency, robustness, and scalability in massive parallel environment of the proposed methods for various physical problems has been achieved. Particular attention has been paid to army related applications including the pedestrian flow problems.
- Numerical Mathematics