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| 1 | Non-oscillatory relaxation methods for the shallow water equations in one and two space dimensions显示文摘 | Seaid M | 2004 | Internation Journal for Numerical Methods in Fluids2004，46，5： | 1 |
| 2 | Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes 显示文摘 | Benkhaldoun F Elmahi I Seaid M | 2007 | Journal of Computational Physics2007，226，2： | 1 |
| 3 | Flux limiters in the coupling of radiation and hydrodynamic models显示文摘 | Seaid M Klar A Dubroca B | 2004 | Journal of Computational and Applied Mathematics2004，168，12： | 1 |
| 4 | Non-oscillatory relaxation methods for theshallow water equations in one and two space dimen-sions显示文摘 | SEAID M | 2004 | International Journal of Numerical Methods inFluids2004，46，5： | 1 |
| 5 | Well balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes 显示文摘 | BENKHALDOUN F ELMAHI I SEAID M | 2007 | Journal of Computational Physics2007，226，2： | 1 |
| 6 | New Finite-Volume Relaxation Methods for the Third-Order Differential Equations显示文摘We propose a new method for numerical solution of the third-order differential equations.The key idea is to use relaxation approximation to transform the nonlinear third-order differential equation to a semilinear second-order differential system with a source term and a relaxation parameter.The relaxation system has linear characteristic variables and can be numerically solved without relying on Riemann problem solvers or linear iterations.A non-oscillatory finite volume method for the relaxation system is developed.The method is uniformly accurate for all relaxation rates.Numerical results are shown for some nonlinear problems such as the Korteweg-de Vires equation.Our method demonstrated the capability of accurately capturing soliton wave phenomena. | Fayssal Benkhaldoun Mohammed Seaid | 2008 | Communications in Computational Physics2008，4，9： | 1 |
| 7 | A simple finite volume method for the shallow water equations 显示文摘 | F Benkhaldoun M Seaid | 2010 | Journal of Computational and Applied Mathematics2010，，234： | 1 |
| 8 | A new finite vol- ume method for flux-gradient and source-term balan- eing in shallow water equations显示文摘 | F Benkhaldoun I Elmahi M Seaid | 2010 | Computer Meth- ods in Applied Mechanics and Engineering2010，，199： | 1 |
| 9 | A flux-limiter method for dam-break fows over erodible sediment beds显示文摘 | Fayssal Benkhaldouna Saida Saria Mohammed Seaid | 2012 | Applied Mathematical Modelling2012，36，： | 1 |
| 10 | A domain decomposition method for conservation laws with discontinuous flux function显示文摘 | Herty M Seaid M Singh A K | 2007 | Applied Numerical Mathematics2007，57，4： | 1 |
| 11 | Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes 显示文摘 | BENKHALDOUN F ELMAHI I SEAID M | 2007 | Journal of Computational Physics2007，226，1： | 1 |
| 12 | Higher-order relaxation schemes for hyperbolic systems of conservation laws显示文摘 | M K Banda M Seaid | 2005 | Journal of Numerical Mathematics2005，，3： | 1 |
| 13 | MULTIDIMENSIONAL RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS显示文摘我们为能量守恒定律的多维的夸张系统构造并且实现一个非摆动的松驰计划。方法转变非线性的夸张系统到半有没有使用 Riemann 解答者或线性重复,能数字地被解决的一个松驰来源术语和线性特征的线性模型。到 discretize 我们在空间和 TVD Runge-Kutta 时间集成考虑高分辨率的重建的松驰系统。计划的详细明确的表达在三种空间尺寸为问题被给,数字实验在数量和系统盒子被实现显示出方法的有效性。数学题目分类:35L60, 35L65, 82B40, 65M20, 74S10, 65L06。 | Mohammed Seaid | 2007 | Journal of Computational Mathematics2007，25，4： | 0 |
| 14 | A Conservative and Monotone Characteristic Finite Element Solver for Three-Dimensional Transport and Incompressible Navier-Stokes Equations on Unstructured Grids显示文摘We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressibleNavier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite elementmethod for the space discretization. This class of computational solvers benefits fromthe geometrical flexibility of the finite elements and the strong stability of the modi-fied method of characteristics to accurately solve convection-dominated flows usingtime steps larger than its Eulerian counterparts. In the current study, we implementthree-dimensional limiters to convert the proposed solver to a fully mass-conservativeand essentially monotonicity-preserving method in addition of a low computationalcost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. Theproposed method is applied to well-established problems for transport and incompressible Navier-Stokes equations in three space dimensions. The numerical resultsillustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominatedflow problems on unstructured tetrahedral meshes. | Bassou Khouya Mofdi El-Amrani Mohammed Seaid | 2022 | Communications in Computational Physics2022，31，1： | 0 |
| 15 | Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows显示文摘We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows.The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis forces.The thermal effects are incorporated in the momentum equation by using a Boussinesq approximation.The dispersion of free-surface temperature is modelled by an advection-diffusion equation.Two distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice structure.Neither upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water equations.In addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source terms.We validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar. | Mohammed Seaid Guido Thommes | 2009 | Advances in Applied Mathematics and Mechanics2009，1，3： | 0 |
| 16 | A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer ShallowWater Equations with Non-Flat Bottom Topography显示文摘A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography.The governing equations are reformulated as a non-linear system of conservation laws with differential source forces and reaction terms.Coupling between theflow layers is accounted for in the system using a set of ex-change relations.The considered well-balanced Runge-Kutta discontinuous Galerkin method is a locally conservativefinite element method whose approximate solutions are discontinuous across the inter-element boundaries.The well-balanced property is achieved using a special discretization of source terms that depends on the nature of hydrostatic solutions along with the Gauss-Lobatto-Legendre nodes for the quadra-ture used in the approximation of source terms.The method can also be viewed as a high-order version of upwindfinite volume solvers and it offers attractive features for the numerical solution of conservation laws for which standardfinite element methods fail.To deal with the source terms we also implement a high-order splitting operator for the time integration.The accuracy of the proposed Runge-Kutta discontinuous Galerkin method is examined for several examples of multilayer free-surfaceflows over bothflat and non-flat beds.The performance of the method is also demonstrated by comparing the results obtained using the proposed method to those obtained using the incompressible hydrostatic Navier-Stokes equations and a well-established kinetic method.The proposed method is also applied to solve a recirculationflow problem in the Strait of Gibraltar. | Nouh Izem Mohammed Seaid | 2022 | Advances in Applied Mathematics and Mechanics2022，14，3： | 0 |
| 17 | Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement显示文摘We propose a high-order enriched partition of unity finite element method for linear and nonlinear time-dependent diffusion problems.The solution of this class of problems often exhibits non-smooth features such as steep gradients and boundary layers which can be very challenging to recover using the conventional low-order finite element methods.A class of steady-state exponential functions has been widely used for enrichment and its performance to numerically solve these challenges has been demonstrated.However,these enrichment functions have been used only in context of the standard h-version refinement or the so-called q-version refinement.In this paper we demonstrate that the p-version refinement can also be a very attractive option in terms of the efficiency and the accuracy in the enriched partition of unity finite element method.First,the transient diffusion problem is integrated in time using a semi-implicit scheme and the semi-discrete problem is then integrated in space using the p-version enriched finite elements.Numerical results are presented for three test examples of timedependent diffusion problems in both homogeneous and heterogeneous media.The computed results show the significant improvement when using the p-version refined enriched approximations in the finite element analysis.In addition,these results support our expectations for a robust and high-order accurate enriched partition of unity finite element method. | Abdelkarim El Kahoui Mustapha Malek Nouh Izem MShadi Mohamed Mohammed Seaid | 2020 | Computer Modeling in Engineering & Sciences2020，，7： | 0 |
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