|
| ||
|
|
||
Boundary Discretization (boundary + discretization)
Selected AbstractsThe boundary element method for solving the Laplace equation in two-dimensions with oblique derivative boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007D. Lesnic Abstract In this communication, we extend the Neumann boundary conditions by adding a component containing the tangential derivative, hence producing oblique derivative boundary conditions. A variant of Green's formula is employed to translate the tangential derivative to the fundamental solution in the boundary element method (BEM). The two-dimensional steady-state heat conduction with the imposed oblique boundary condition has been tested in smooth, piecewise smooth and multiply connected domains in which the Laplace equation is the governing equation, producing results at the boundary in excellent agreement with the available analytical solutions. Convergence of the normal and tangential derivatives at the boundary is also achieved. The numerical boundary data are then used to successfully calculate the values of the solution at interior points again. The outlined test cases have been repeated with various boundary element meshes, indicating that the accuracy of the numerical results increases with increasing boundary discretization. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006J. Burguete Abstract A revision of some well-known discretization techniques for the numerical boundary conditions in 1D shallow-water flow models is presented. More recent options are also considered in the search for a fully conservative technique that is able to preserve the good properties of a conservative scheme used for the interior points. Two conservative numerical schemes are used as representatives of the families of explicit and implicit numerical methods. The implementation of the different boundary options to these schemes is compared by means of the simulation of several test cases with exact solution. The schemes with the global conservation boundary discretization are applied to the simulation of a real river flood wave leading to very satisfactory results. Copyright © 2005 John Wiley & Sons, Ltd. [source] Null-field approach for Laplace problems with circular boundaries using degenerate kernelsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Jeng-Tzong Chen Abstract In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Geometrical interpretation of the multi-point flux approximation L-methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Yufei Cao Abstract In this paper, we first investigate the influence of different Dirichlet boundary discretizations on the convergence rate of the multi-point flux approximation (MPFA) L-method by the numerical comparisons between the MPFA O- and L-method, and show how important it is for this new method to handle Dirichlet boundary conditions in a suitable way. A new Dirichlet boundary strategy is proposed, which in some sense can well recover the superconvergence rate of the normal velocity. In the second part of the work, the MPFA L-method with homogeneous media is studied. A systematic concept and geometrical interpretations of the L-method are given and illustrated, which yield more insight into the L-method. Finally, we apply the MPFA L-method for two-phase flow in porous media on different quadrilateral grids and compare its numerical results for the pressure and saturation with the results of the two-point flux approximation method. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||