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High order numerical methods for PDEs, such as spectral methods, weighted essentially non-oscillatory (WENO) methods and discontinuous Galerkin (DG) methods.

Structure-preserving methods for nonlinear wave equations, shallow water equations, and Euler equations, etc.

Model and simulation of the pedestrian flows, multiphase flows, and gradient flows, etc.

Efficient time discretization methods.

Arbitrary Lagrangian-Eulerian methods for moving domain problems.