The Experts below are selected from a list of 132 Experts worldwide ranked by ideXlab platform
Vincenzo Casulli - One of the best experts on this subject based on the ideXlab platform.
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semi implicit finite difference methods for the two dimensional shallow water Equation
Journal of Computational Physics, 1990Co-Authors: Vincenzo CasulliAbstract:Abstract In this paper a semi-implicit finite difference method for the 2-dimensional shallow water Equations is derived and discussed. A characteristic analysis of the governing Equations is carried out first, in order to determine those terms to be discretized implicitly so that the stability of the method will not depend upon the celerity. Such terms are the gradient of the water surface elevation in the momentum Equations and the velocity divergence in the continuity Equation. The convective terms are discretized explicitly. The simpler explicit discretization for the convective terms is the upwind discretization which is conditionally stable and introduces some artificial viscosity. It is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an Eulerian-Lagrangian approach with large time steps is used to discretize the convective terms. This method, at each time step, requires the solution of a linear, symmetric, 5-diagonal system. Such a system is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere. Thus, existence and uniqueness of the numerical solution is assured. The resulting algorithm is mass conservative and fully vectorizable for an efficient implementation on modern vector computers. The performance of this method is further improved when used in combination with an ADI technique which results in two sets of simpler, linear 3-diagonal systems and maintains all the properties described above.
Clint Scovel - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian truncation of the shallow water Equation
Letters in Mathematical Physics, 1994Co-Authors: Ge Zhong, Clint ScovelAbstract:In this Letter, we describe a truncation of the Eulerian description of the shallow water Equation of climate modeling to a finite-dimensional Hamiltonian system. The technique is to use an isomorphism from a semidirect product Poisson manifold to a direct product of Poisson manifolds, both of whose components are truncatable to finite-dimensional Poisson manifolds, based on Moser's theorem on volume elements.
Ge Zhong - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian truncation of the shallow water Equation
Letters in Mathematical Physics, 1994Co-Authors: Ge Zhong, Clint ScovelAbstract:In this Letter, we describe a truncation of the Eulerian description of the shallow water Equation of climate modeling to a finite-dimensional Hamiltonian system. The technique is to use an isomorphism from a semidirect product Poisson manifold to a direct product of Poisson manifolds, both of whose components are truncatable to finite-dimensional Poisson manifolds, based on Moser's theorem on volume elements.
Adrian Constantin - One of the best experts on this subject based on the ideXlab platform.
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Least Action Principle for an Integrable Shallow Water Equation
Journal of Nonlinear Mathematical Physics, 2020Co-Authors: Adrian Constantin, Boris KolevAbstract:For an integrable shallow water Equation we describe a geometrical approach showing that any two nearby fluid configurations are successive states of a unique flow minimizing the kinetic energy.
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Orbital stability of solitary waves for a shallow water Equation
Physica D: Nonlinear Phenomena, 2001Co-Authors: Adrian Constantin, Luc MolinetAbstract:We prove the orbital stability of the solitary waves for a shallow water Equation by means of variational methods, considering a minimization problem with an appropriate constraint.
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existence of permanent and breaking waves for a shallow water Equation a geometric approach
Annales de l'Institut Fourier, 2000Co-Authors: Adrian ConstantinAbstract:On obtient des theoremes d'existence de solutions globales en temps et des resultats sur la formation (le signularites pour une Equation qui modelise le phenomene des ondes de surface en eau peu profonde. La solution peut exploser uniquement sous la forme d'un deferlement. En utilisant le fait que cette Equation d'ondes decrit le flot geodesique du groupe des diffeomorphismes de la droite verifiant certaines conditions asymptotiques a l'infini, muni d'une structure de variete riemannienne, on donne des conditions suffisantes sur la donnee initiale pour que la solution soit globale en temps ou bien qui impliquent un deferlement au bout d'un temps fini. Ces resultats se traduisent en terme de proprietes des geodesiques du groupe des diffeomorphismes.
Nursalasawati Rusli - One of the best experts on this subject based on the ideXlab platform.
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Semi-implicit method for solving one dimensional shallow water Equation
2016Co-Authors: Siti Maryam Hafiza Mohd Kanafiah, Nursalasawati RusliAbstract:Shallow water Equation is widely implemeted in handling fluid flow problems. This paper presents deployment of semi-implicit method to solve one dimensional coupled shallow water Equation. The boundary condition, initial condition, space step, time step and the approximation of shallow water Equation are programmed and executed in MATLAB to form a numerical solution. This numerical procedure is described in staggered grid scheme. Semi-implicit formulation is validated by using the θ -method for free surface wave damping problem. From the validation result, it has been proved that the shallow water Equation can be solved using semi-implicit method.