The mixed spectral finite-difference (MSFD) model: Improved upper boundary conditions

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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Biharmonic navigation using radial basis functions

Robotica ◽

10.1017/s0263574721000709 ◽

2021 ◽

pp. 1-12

Author(s):

Xu-Qian Fan ◽

Wenyong Gong

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Radial Basis Functions ◽

Real World ◽

Biharmonic Equation ◽

Finite Difference Methods ◽

Basis Functions ◽

Large Size ◽

Radial Basis ◽

Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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A second-order accurate finite difference scheme for a class of nonlocal parabolic equations with natural boundary conditions

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(96)00097-0 ◽

1996 ◽

Vol 76 (1-2) ◽

pp. 137-146 ◽

Cited By ~ 23

Author(s):

Zhi-Zhong Sun

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Parabolic Equations ◽

Finite Difference Scheme ◽

Second Order ◽

Natural Boundary ◽

Nonlocal Parabolic Equations ◽

Natural Boundary Conditions

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Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

Journal of Applied Mechanics ◽

10.1115/1.3424424 ◽

1978 ◽

Vol 45 (4) ◽

pp. 812-816 ◽

Cited By ~ 1

Author(s):

B. S. Berger ◽

B. Alabi

Keyword(s):

Fourier Transform ◽

Finite Difference ◽

Boundary Conditions ◽

Half Space ◽

Coordinate Transformation ◽

Numerical Results ◽

Three Dimensions ◽

Curvilinear Coordinates ◽

Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

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Absorbing boundary conditions for 3-D acoustic and elastic finite-difference calculations

Bulletin of the Seismological Society of America ◽

10.1785/bssa0790010211 ◽

1989 ◽

Vol 79 (1) ◽

pp. 211-218

Author(s):

Wen-Fong Chang ◽

George A. McMechan

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Absorbing Boundary Conditions ◽

Absorbing Boundary

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Efficient compact finite difference method for variable coefficient fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions in conservative form

Computational and Applied Mathematics ◽

10.1007/s40314-018-0690-7 ◽

2018 ◽

Vol 37 (5) ◽

pp. 6252-6269 ◽

Cited By ~ 3

Author(s):

Lei Ren ◽

Lei Liu

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Boundary Conditions ◽

Difference Method ◽

Variable Coefficient ◽

Neumann Boundary ◽

Neumann Boundary Conditions ◽

Diffusion Equations ◽

Compact Finite Difference Method ◽

Conservative Form

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Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions

PLoS ONE ◽

10.1371/journal.pone.0206235 ◽

2018 ◽

Vol 13 (10) ◽

pp. e0206235 ◽

Cited By ~ 1

Author(s):

Vyacheslav A. Trofimov ◽

Evgeny M. Trykin

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Artificial Boundary ◽

Artificial Boundary Conditions ◽

Rosenbrock Method ◽

Implicit Finite Difference

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Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽

10.1190/1.1440881 ◽

1978 ◽

Vol 43 (6) ◽

pp. 1099-1110 ◽

Cited By ~ 169

Author(s):

Albert C. Reynolds

Keyword(s):

Wave Propagation ◽

Reflection Coefficient ◽

Finite Difference ◽

Boundary Conditions ◽

Numerical Solution ◽

Neumann Boundary ◽

Synthetic Seismograms ◽

Neumann Boundary Conditions ◽

Numerical Calculations ◽

Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

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