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High-resolution rotated grid method for conservation laws with embedded geometries
We develop a second-order rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using an underlying Cartesian grid. Stability for time steps adequate for the regular part of the grid is obtained by increasing the domain of dependence of the numerical method ...
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions
(Society for Industrial and Applied Mathematics, 2002)
We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where the flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function fi(q) over the ith grid cell and leading to a generalized Riemann problem between ...