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Mohammed Seaïd - One of the best experts on this subject based on the ideXlab platform.

  • A Conservative Semi-Lagrangian Finite Volume Method for Convection–Diffusion Problems on Unstructured Grids
    Journal of Scientific Computing, 2020
    Co-Authors: Ilham Asmouh, Mohammed Seaïd, Mofdi El-amrani, Naji Yebari
    Abstract:

    A conservative semi-Lagrangian Finite Volume Method is presented for the numerical solution of convection–diffusion problems on unstructured grids. The new Method consists of combining the modified Method of characteristics with a cell-centered Finite Volume discretization in a fractional-step manner where the convection part and the diffusion part are treated separately. The implementation of the proposed semi-Lagrangian Finite Volume Method differs from its Eulerian counterpart in the fact that the present Method is applied at each time step along the characteristic curves rather than in the time direction. To ensure conservation of mass at each time step, we adopt the adjusted advection techniques for unstructured triangular grids. The focus is on constructing efficient solvers with large stability regions and fully conservative to solve convection-dominated flow problems. We verify the performance of our semi-Lagrangian Finite Volume Method for a class of advection–diffusion equations with known analytical solutions. We also present numerical results for a transport problem in the Mediterranean sea.

  • Projection Finite Volume Method for shallow water flows
    Mathematics and Computers in Simulation, 2015
    Co-Authors: Fayssal Benkhaldoun, Saida Sari, Mohammed Seaïd
    Abstract:

    A simple and accurate projection Finite Volume Method is developed for solving shallow water equations in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstructed using the Method of characteristics, while an Eulerian Method is used to discretize the conservation equations in a Finite Volume framework. The Method is conservative and it combines advantages of the Method of characteristics to accurately solve the shallow water flows with an Eulerian Finite Volume Method to discretize the equations. Numerical results are presented for several applications in rotating shallow water problems. The aim of such a Method compared to the conventional Finite Volume Methods is to solve shallow water equations efficiently and with an appropriate level of accuracy.

  • A simple Finite Volume Method for the shallow water equations
    Journal of Computational and Applied Mathematics, 2010
    Co-Authors: Fayssal Benkhaldoun, Mohammed Seaïd
    Abstract:

    We present a new Finite Volume Method for the numerical solution of shallow water equations for either flat or non-flat topography. The Method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the Method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed Finite Volume Method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed Finite Volume Method is verified against several benchmark tests and shows good agreement with analytical solutions.

Sudi Mungkasi - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids
    Advances in Mathematical Physics, 2016
    Co-Authors: Sudi Mungkasi
    Abstract:

    This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a Finite Volume Method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh Finite Volume Method, as the Method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

  • A Finite Volume Method for shallow water flows on triangular computational grids
    2011
    Co-Authors: Sudi Mungkasi, Stephen Roberts
    Abstract:

    This paper presents a Finite Volume Method used to solve the two-dimensional shallow water (wave) equations and how the Finite Volume Method is implemented in ANUGA software. This Finite Volume Method is the numerical Method underlying the software. ANUGA is open source software developed by Australian National University (ANU) and Geoscience Australia (GA). This software uses the Finite Volume Method with triangular domain discretisation for the computation. Three test cases are considered in order to evaluate the performance of the software. Overall, ANUGA is a robust software to simulate two-dimensional shallow water flows.

S. Muzaferija - One of the best experts on this subject based on the ideXlab platform.

  • Finite Volume Method for simulation of extrusion processes
    International Journal for Numerical Methods in Engineering, 2005
    Co-Authors: S. Muzaferija
    Abstract:

    In this paper, the development of a Finite Volume Method for prediction of plastic flow of metals during cold and hot extrusion processes is described. The Method solves the equations governing mass, momentum and heat balance in their integral form, using discretization elements of an arbitrary polyhedral shape. Comparisons of the numerical and experimental results show a very good agreement, implying that the proposed numerical Method can be used as a useful tool in designing extrusion processes.

  • COMPUTATION OF FREE-SURFACE FLOWS USING THE Finite-Volume Method AND MOVING GRIDS
    Numerical Heat Transfer Part B-fundamentals, 1997
    Co-Authors: S. Muzaferija
    Abstract:

    Abstract This article outlines the development and application of an interface-tracking algorithm for computation of free-surface flows using the Finite-Volume Method and moving grids. The kinematic boundary condition and the space conservation law are used to determine the position and shape of the free-surface interface. Several test cases are selected to demonstrate the Method's accuracy and applicability for calculation of two- and three-dimensional free-surface flows. The approach can easily be implemented in any existing Finite-Volume Method using either structured or unstructured grids.

Fayssal Benkhaldoun - One of the best experts on this subject based on the ideXlab platform.

  • Projection Finite Volume Method for shallow water flows
    Mathematics and Computers in Simulation, 2015
    Co-Authors: Fayssal Benkhaldoun, Saida Sari, Mohammed Seaïd
    Abstract:

    A simple and accurate projection Finite Volume Method is developed for solving shallow water equations in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstructed using the Method of characteristics, while an Eulerian Method is used to discretize the conservation equations in a Finite Volume framework. The Method is conservative and it combines advantages of the Method of characteristics to accurately solve the shallow water flows with an Eulerian Finite Volume Method to discretize the equations. Numerical results are presented for several applications in rotating shallow water problems. The aim of such a Method compared to the conventional Finite Volume Methods is to solve shallow water equations efficiently and with an appropriate level of accuracy.

  • A simple Finite Volume Method for the shallow water equations
    Journal of Computational and Applied Mathematics, 2010
    Co-Authors: Fayssal Benkhaldoun, Mohammed Seaïd
    Abstract:

    We present a new Finite Volume Method for the numerical solution of shallow water equations for either flat or non-flat topography. The Method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the Method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed Finite Volume Method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed Finite Volume Method is verified against several benchmark tests and shows good agreement with analytical solutions.

Ian Turner - One of the best experts on this subject based on the ideXlab platform.

  • a novel Finite Volume Method for the riesz space distributed order diffusion equation
    Computers & Mathematics With Applications, 2017
    Co-Authors: Fawang Liu, Libo Feng, Ian Turner
    Abstract:

    Abstract In recent years, considerable attention has been devoted to distributed-order differential equations mainly because they appear to be more effective for modelling complex processes which obey a mixture of power laws or flexible variations in space. In this paper, we propose a novel Finite Volume Method (FVM) for a distributed-order space-fractional diffusion equation (FDE). Firstly, we use the mid-point quadrature rule to transform the space distributed-order diffusion equation into a multi-term fractional equation. Secondly, the transformed multi-term fractional equation is solved by discretising in space using the Finite Volume Method and then in time using the Crank–Nicolson scheme. Thirdly, we prove that the Crank–Nicolson scheme with FVM is unconditionally stable and convergent with second order accuracy in both time and space. Finally, two numerical examples are presented to show the effectiveness of the numerical Method. These Methods and techniques can also be used to solve other types of fractional partial differential equations.

  • a novel Finite Volume Method for the riesz space distributed order advection diffusion equation
    Applied Mathematical Modelling, 2017
    Co-Authors: Fawang Liu, Libo Feng, Ian Turner
    Abstract:

    Abstract In this paper, we investigate the Finite Volume Method (FVM) for a distributed-order space-fractional advection–diffusion (AD) equation. The mid-point quadrature rule is used to approximate the distributed-order equation by a multi-term fractional model. Next, the transformed multi-term fractional equation is solved by discretizing in space by the Finite Volume Method and in time using the Crank–Nicolson scheme. We use a novel technique to deal with the convection term, by which the Riesz fractional derivative of order 0 γ

  • a novel Finite Volume Method for the riesz space distributed order advection diffusion equation
    ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS); Science & Engineering Faculty, 2017
    Co-Authors: Fawang Liu, Libo Feng, Ian Turner
    Abstract:

    In this paper, we investigate the Finite Volume Method (FVM) for a distributed-order space-fractional advection–diffusion (AD) equation. The mid-point quadrature rule is used to approximate the distributed-order equation by a multi-term fractional model. Next, the transformed multi-term fractional equation is solved by discretizing in space by the Finite Volume Method and in time using the Crank–Nicolson scheme. We use a novel technique to deal with the convection term, by which the Riesz fractional derivative of order 0 < γ < 1 is transformed into a fractional integral form. An important contribution of our work is the use of nodal basis function to derive the discrete form of our model. The unique solvability of the scheme is also discussed and we prove that the Crank–Nicolson scheme is unconditionally stable and convergent with second-order accuracy. Finally, we give some examples to show the effectiveness of the numerical Method. Keywords Distributed-order equation; Finite Volume Method; Riesz fractional derivatives; Fractional advection–diffusion equation; Stability and convergence