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- W2904453176 abstract "In this work, we present an improvement of the Lagrangian–Eulerian space–time tracking forward scheme to deal with balance laws and related applications. This extended algorithm is shown in the most simple setting and it is a result of our previous works. We describe and explain a new strategy of discretization of conservation laws, starting from the scalar case in one space dimension, extending it to systems and to the multi-dimensional setting. The computations are fast, accurate and stable with good resolution. This algorithm is very easy to implement in a computer to address the delicate well-balancing between the first-order hyperbolic flux and the source term. We do not use approximate or exact Riemann solvers, nonlinear reconstructions, or upwind source term discretizations. The scheme is written into the classical theory of monotone schemes, which produces a scheme that converges to entropy solutions linked to the purely hyperbolic counterpart. This method can produce well-balanced approximations of solutions for nonlinear balance laws. Numerical experiments also demonstrate the robustness of the forward tracking to solve related problems involving systems and two-dimensional models." @default.
- W2904453176 created "2018-12-22" @default.
- W2904453176 creator A5061670114 @default.
- W2904453176 creator A5085399038 @default.
- W2904453176 date "2019-05-01" @default.
- W2904453176 modified "2023-10-03" @default.
- W2904453176 title "A fast, robust, and simple Lagrangian–Eulerian solver for balance laws and applications" @default.
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- W2904453176 doi "https://doi.org/10.1016/j.camwa.2018.12.019" @default.
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