Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods
by Randall J. LeVeque and Keh-Ming Shyue, J. Comput. Phys., 123 (1996), 354-368.

Abstract. We present a fully conservative, high resolution approach to front tracking for nonlinear systems of conservation laws in two space dimensions. An underlying uniform Cartesian grid is used, with some cells cut by the front into two subcells. The front is moved by solving a Riemann problem normal to each segment of the front and using the motion of the strongest wave to give an approximate location of the front at the end of the time step. A high resolution finite volume method is then applied on the resulting slightly irregular grid to update all cell values. A "large time step" wave propagation algorithm is used that remains stable in the small cut cells with a time step that is chosen with respect to the uniform grid cells. Numerical results on a radially symmetric problem show that pointwise convergence with order between 1 and 2 is obtained in both the cell values and location of the front. Other computations are also presented.

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