Exact solutions of the system of nonlinear shallow water equations on paraboloid are constructed by the method of group analysis. These solutions describe fast wave motion of the fluid layer and slow evolution of symm...
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Exact solutions of the system of nonlinear shallow water equations on paraboloid are constructed by the method of group analysis. These solutions describe fast wave motion of the fluid layer and slow evolution of symmetric localized vortices. Explicit formulae are obtained for asymptotic solution related to the linear shallow water approximation. numericalmethods are used by the modeling the trajectory of the vortex center in the case of asymmetric vortices.
In this paper we examine a numerical implementation of Fokas' unified method for elliptic boundary value problems on convex polygons. Within this setting the unified method provides a reconstruction of the unknown...
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In this paper we examine a numerical implementation of Fokas' unified method for elliptic boundary value problems on convex polygons. Within this setting the unified method provides a reconstruction of the unknown boundary values from the known boundary data for an important class of elliptic boundary value problems. We demonstrate that this approach can be used to study the classical Dirichlet eigenvalue problem for the Laplacian on convex polygons. We show that this problem is equivalent to a nonlinear eigenvalue problem for a semi-Fredholm operator which has holomorphic dependence on the eigenvalue itself. We also study the classical Dirichlet problem for the Helmholtz operator. We provide a new Galerkin scheme for the underlying Dirichlet-Neumann map, and prove that for sufficiently regular Dirichlet data this scheme converges with spectral accuracy. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.
A bed-load sediment transport model is used to describe realistic cases of the morphodynamics in coastal areas. The hydrodynamic equations are based on the well-known, two-dimensional depth-averaged non-linear shallow...
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A bed-load sediment transport model is used to describe realistic cases of the morphodynamics in coastal areas. The hydrodynamic equations are based on the well-known, two-dimensional depth-averaged non-linear shallow water equations, with bathymetry forces and friction, which are subsequently coupled to the Exner equation to describe the morphological evolution. Different forms of the bed-load transport flux are considered in the Exner equation and certain relations between them are established. The numerical model is expressed in a fully-coupled form where a single system of equations is solved by a high resolution two-dimensional finite volume scheme of the relaxation type. The relaxation is performed by classical models where neither approximate Riemann solvers nor characteristic decompositions are needed. The overall numerical scheme is validated in benchmark problems, and for a realistic application of a coastal area on the northern side of the island of Crete. The validity of these results is established by comparisons made with the well-known MIKE Software by DHI Group. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
This book gathers a selection of invited and contributed lectures from the European conference on numerical Mathematics and Advanced applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provide...
ISBN:
(纸本)9783319383835
This book gathers a selection of invited and contributed lectures from the European conference on numerical Mathematics and Advanced applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numericallinearalgebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.
Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting...
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ISBN:
(纸本)9781538639542
Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some intelligent data analysis tools on the samples. These problems are commonly referred to as inverse source problems. This work presents a novel framework for solving such inverse source problem for linear PDEs by drawing from certain recent results in modern sampling theory. Under the new framework, we study the well-known diffusion PDE and present numerical results that highlight the validity and robustness of the approach.
The proceedings contain 62 papers. The special focus in this conference is on Space Discretizationmethods for PDEs, Finite Element methods, Discontinuous Galerkin methods for PDEs, numericallinearalgebra, High Perfo...
ISBN:
(纸本)9783319399270
The proceedings contain 62 papers. The special focus in this conference is on Space Discretizationmethods for PDEs, Finite Element methods, Discontinuous Galerkin methods for PDEs, numericallinearalgebra, High Performance Computing, Reduced Order Modeling, Problems with Singularities and Miscellaneous Topics. The topics include: DRBEM Solution of the double diffusive convective flow;second order implicit schemes for scalar conservation laws;on the full and global accuracy of a compact third order WENO scheme;how to avoid mass matrix for linear hyperbolic problems;finite elements for the navier-stokes problem with outflow condition;numerical experiments for multiscale problems in linear elasticity;the skeleton reduction for finite element substructuring methods;stable discontinuous galerkin FEMWithout penalty parameters;semi-implicit DGM applied to a model of flocking;a posteriori error estimates for nonstationary problems;a simple proposal for parallel computation over time of an evolutionary process with implicit time stepping;model reduction formultiscale lithium-ion battery simulation;reduced-order multiobjective optimal control of semilinear parabolic problems;a local error estimate for the Poisson equation with a line source term;CFD Simulation of interaction between a fluid and a vibrating profile;drag reduction via phase randomization in turbulent pipe flow;finite volume scheme for modeling of NAPL vapor transport in air;numerical solution of constrained curvature flow for closed planar curves;a Riemannian BFGS method for nonconvex optimization problems and discrete lie derivative.
This note deals with the static output feedback stabilization problem of linear time-invariant (LTI) systems, one of the most relevant open problems in the field of control theory. We present a new sufficient linear m...
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The European conferences on numerical Mathematics and Advanced applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and chall...
ISBN:
(纸本)9783662511299
The European conferences on numerical Mathematics and Advanced applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numericallinearalgebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
Computational fluid dynamics (CFD) uses numerical analysis methods and algorithms to solve and analyze problems that involve fluid flows. These algorithms require very high computational power that does not exist in t...
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