A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions
Copyright policy )A fast second-order discretization scheme for the linearized Green-Naghdi system with absorbing boundary conditions
In this paper, we present a fully discrete second-order finite-difference scheme with fast evaluation of the convolution involved in the absorbing boundary conditions to solve the one-dimensional linearized Green-Naghdi system. The Padé expansion of the square-root function in the complex plane is used to implement the fast convolution. By introducing a constant damping parameter into the governing equations, the convergence analysis is developed when the damping term fulfills some conditions. In addition, the scheme is stable and leads to a highly reduced computational cost and low memory storage. A numerical example is provided to support the theoretical analysis and to illustrate the performance of the fast numerical scheme.
- French Institute for Research in Computer Science and Automation France
- UNIVERSITE DE LORRAINE France
- University of Lorraine France
- Peking University China (People's Republic of)
- Hebei University China (People's Republic of)
Square root, Economics, Computational Mechanics, Free-surface potential flows for incompressible inviscid fluids, Evolutionary biology, Finite difference methods applied to problems in fluid mechanics, Engineering, Convolution (computer science), Convergence analysis, Numerical Methods for Singularly Perturbed Problems, Finite difference methods for initial value and initial-boundary value problems involving PDEs, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Numerical Analysis, PDE-Constrained Optimization, linearized Green-Naghdi system, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Programming language, Stabilized Methods, Function (biology), Physical Sciences, Convergence (economics), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite Difference Schemes, Artificial neural network, Geometry, Adaptive Mesh Refinement, absorbing boundary conditions, Mathematical analysis, convergence analysis, convolution quadrature, Finite Element Methods for Fluid-Structure Interaction, fast algorithm, Machine learning, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Electrical and Electronic Engineering, Padé approximation, Biology, Economic growth, Scheme (mathematics), Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Square (algebra), dispersive water wave, Applied mathematics, Computer science, free-surface Euler equations, fully discrete finite difference scheme, Boundary (topology), Finite-Difference Time-Domain Methods in Electromagnetics, Mathematics, Discretization, Constant (computer programming)
Square root, Economics, Computational Mechanics, Free-surface potential flows for incompressible inviscid fluids, Evolutionary biology, Finite difference methods applied to problems in fluid mechanics, Engineering, Convolution (computer science), Convergence analysis, Numerical Methods for Singularly Perturbed Problems, Finite difference methods for initial value and initial-boundary value problems involving PDEs, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, Numerical Analysis, PDE-Constrained Optimization, linearized Green-Naghdi system, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Programming language, Stabilized Methods, Function (biology), Physical Sciences, Convergence (economics), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite Difference Schemes, Artificial neural network, Geometry, Adaptive Mesh Refinement, absorbing boundary conditions, Mathematical analysis, convergence analysis, convolution quadrature, Finite Element Methods for Fluid-Structure Interaction, fast algorithm, Machine learning, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Electrical and Electronic Engineering, Padé approximation, Biology, Economic growth, Scheme (mathematics), Water waves, gravity waves; dispersion and scattering, nonlinear interaction, Square (algebra), dispersive water wave, Applied mathematics, Computer science, free-surface Euler equations, fully discrete finite difference scheme, Boundary (topology), Finite-Difference Time-Domain Methods in Electromagnetics, Mathematics, Discretization, Constant (computer programming)
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