Construction of explicit and implicit symmetric tvd schemes and their applications
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
TVD Fluxes for the High-Order ADER Schemes
Journal of Scientific Computing
Conservative Models and Numerical Methods for Compressible Two-Phase Flow
Journal of Scientific Computing
A new coupled fluid-structure modeling methodology for running ductile fracture
Computers and Structures
Modeling and numerical approximation of a 2.5D set of equations for mesoscale atmospheric processes
Journal of Computational Physics
The DFLU flux for systems of conservation laws
Journal of Computational and Applied Mathematics
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Numerical methods for conservation laws constructed in the framework of finite volume and discontinuous Galerkin finite elements require, as the building block, a monotone numerical flux. In this paper we present some preliminary results on the MUSTA approach [E.F. Toro, Multi-stage predictor-corrector fluxes for hyperbolic equations, Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003] for constructing upwind numerical fluxes. The scheme may be interpreted as an un-conventional approximate Riemann solver that has simplicity and generality as its main features. When used in its first-order mode we observe that the scheme achieves the accuracy of the Godunov method used in conjunction with the exact Riemann solver, which is the reference first-order method for hyperbolic systems. At least for the scalar model hyperbolic equation, the Godunov scheme is the best of all first-order monote schemes, it has the smallest truncation error. Extensions of the scheme of this paper are realized in the framework of existing approaches. Here we present a second-order TVD (TVD for the scalar case) extension and show numerical results for the two-dimensional Euler equations on non-Cartesian geometries. The schemes find their best justification when solving very complex systems for which the solution of the Riemann problem, in the classical sense, is too complex, too costly or is simply unavailable.