Home About us Contact
|
Home About us Contact | ||
|
|
||
Order Accurate (order + accurate)
Selected AbstractsA class of higher order compact schemes for the unsteady two-dimensional convection,diffusion equation with variable convection coefficientsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002Jiten C. Kalita Abstract A class of higher order compact (HOC) schemes has been developed with weighted time discretization for the two-dimensional unsteady convection,diffusion equation with variable convection coefficients. The schemes are second or lower order accurate in time depending on the choice of the weighted average parameter , and fourth order accurate in space. For 0.5,,,1, the schemes are unconditionally stable. Unlike usual HOC schemes, these schemes are capable of using a grid aspect ratio other than unity. They efficiently capture both transient and steady solutions of linear and nonlinear convection,diffusion equations with Dirichlet as well as Neumann boundary condition. They are applied to one linear convection,diffusion problem and three flows of varying complexities governed by the two-dimensional incompressible Navier,Stokes equations. Results obtained are in excellent agreement with analytical and established numerical results. Overall the schemes are found to be robust, efficient and accurate. Copyright © 2002 John Wiley & Sons, Ltd. [source] An economical difference scheme for heat transport equation at the microscale,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2004Zhiyue Zhang Abstract Heat transport at the microscale is of vital importance in microtechnology applications. In this article, we proposed a new ADI difference scheme of the Crank-Nicholson type for heat transport equation at the microscale. It is shown that the scheme is second order accurate in time and in space in the H1 norm. Numerical result implies that the theoretical analysis is correct and the scheme is effective. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source] On the finite-differences schemes for the numerical solution of two dimensional Schrödinger equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2002Murat Suba Abstract In this study three different finite-differences schemes are presented for numerical solution of two-dimensional Schrödinger equation. The finite difference schemes developed for this purpose are based on the (1, 5) fully explicit scheme, and the (5, 5) Noye-Hayman fully implicit technique, and the (3, 3) Peaceman and Rachford alternating direction implicit (ADI) formula. These schemes are second order accurate. The results of numerical experiments are presented, and CPU times needed for this problem are reported. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 752,758, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10029. [source] An efficient HOC scheme for transient convection-diffusion-reaction equations with discontinuous coefficients and singular source termsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Rajendra K Ray In this paper, we propose a new methodology for numerically solving one-dimensional (1D) transient convection-diffusion-reaction equations with discontinuous coefficients and singular source terms on nonuniform space grids. This Higher Order Compact (HOC) formulation is at least third order accurate at regular grid points and exactly third order accurate at points just next to the discontinuity. We conduct numerous numerical studies on a number of problems and compare our results with those obtained with immersed interface and other well-known methods. In all cases our formulation is found to produce better results on relatively coarser grids. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||