Von Neumann stability conditions for the convection-diffusion equation

نویسنده

  • P. Wesseling
چکیده

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-di usion equation. Spatial discretization is by the -scheme or the fourth order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for ow computations, and for which, with few exceptions, no su cient von Neumann stability results were available.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerical investigation of the parabolic mixed derivative diffusion equation via Alternating Direction Implicit methods

In this dissertation, we investigate the parabolic mixed derivative diffusion equation modeling the viscous and viscoelastic effects in a non-Newtonian viscoelastic fluid. The model is analytically considered using Fourier and Laplace transformations. The main focus of the dissertation, however, is the implementation of the Peaceman-Rachford Alternating Direction Implicit method. The one-dimens...

متن کامل

Exponential B-Spline Solution of Convection-Diffusion Equations

We present an exponential B-spline collocation method for solving convection-diffusion equation with Dirichlet’s type boundary conditions. The method is based on the Crank-Nicolson formulation for time integration and exponential B-spline functions for space integration. Using the Von Neumann method, the proposed method is shown to be unconditionally stable. Numerical experiments have been cond...

متن کامل

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

متن کامل

Time Implicit High-Order Discontinuous Galerkin Method with Reduced Evaluation Cost

An efficient and robust time integration procedure for a high-order discontinuous Galerkin method is introduced for solving nonlinear second-order partial differential equations. The time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term. The procedure uses an iterative algorithm with reduced evaluation cost. The size o...

متن کامل

Homogenization of convection-diffusion equation in infinite cylinder

The paper deals with a periodic homogenization problem for a non-stationary convection-diffusion equation stated in a thin infinite cylindrical domain with homogeneous Neumann boundary condition on the lateral boundary. It is shown that homogenization result holds in moving coordinates, and that the solution admits an asymptotic expansion which consists of the interior expansion being regular i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995