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Your search keyword '"Touma, Rony"' showing total 2 results
Start Over Author "Touma, Rony" Topic riemann-hilbert problems
2 results on '"Touma, Rony"'

1. Combining a Central Scheme with the Subtraction Method for Shallow Water Equations.

Author

Touma, Rony, Malaeb, Elissa, and Klingenberg, Christian

Subjects
FINITE volume method, SHALLOW-water equations, RIEMANN-Hilbert problems
Abstract

We present a new numerical scheme that is a well-balanced and second-order accurate for systems of shallow water equations (SWEs) with variable bathymetry. We extend in this paper the subtraction method (resulting in well-balancing) to the case of unstaggered central finite volume methods that computes the numerical solution on a single grid. In addition, the proposed scheme avoids solving Riemann problems occurring at cell boundaries as it employs intermediately a layer of ghost-staggered cells. The proposed numerical scheme is then implemented and validated. We successfully manage to solve classical SWE problems from the literature featuring steady states and other equilibria. The results of the study are consistent with previous research, which supports the use of the proposed method to solve SWEs. [ABSTRACT FROM AUTHOR]

Published
2024
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2. An Unstaggered Central Finite Volume Method for the Numerical Approximation of Mixture Flows.

Author

Touma, Rony and Zeidan, Dia

Subjects
*RIEMANN-Hilbert problems, *TWO-phase flow, *MIXTURES, *GRID cells
Abstract

In this work we extend a previously developed unstaggered central finite volume method to the one-dimensional system of mixture two-phase flow problems. The numerical scheme is characterized by its simplicity and robustness as it evolves a piecewise linear numerical solution on a single grid and avoids the resolution of Riemann problems appearing at the faces of the control cells. The strategy consists of employing a second layer of staggered dual cells, on which the numerical solution is evolved at an intermediate time step before being projected back onto the cells of the original grid. The finite volume method is then implemented and used to solve classical mixture flow problems from the recent literature. The obtained numerical results are displayed; they confirm the potential of the unstaggered central scheme to properly and accurately solve mixture two-phase flow systems. [ABSTRACT FROM AUTHOR]

Published
2020
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