Positive Difference Scheme Research Articles

Aproksymacja zagadnienia Dirichleta siatką nierównomierną na brzegu

The author describes a construction of the positive difference scheme, which is the approximation of the Dirichlet problem for an elliptic second order equation with mixed derivatives in an arbitrary region in R2. The a priori estimation for the approximate solution is proved and the estimation of the rate of convergence in maximum norm is established.

Fitted finite volume positive difference scheme for a stationary model of air pollution

A new approach is proposed for the numerical solution of boundary value one-dimensional problem of advection-diffusion equation which arises, among others, in air pollution modeling. Since the problem is posed in an unbounded interval we use a log-transformation to confine the computational region. We discuss the well-posedness of the new problem and the properties of its solution. We derive a positive finite volume difference scheme. Some results from computational experiments are presented.

Adequate numerical solution of air pollution problems by positive difference schemes on unbounded domains

In this work we deal with the numerical solution of some problems of air pollution. Since the problems are posed on unbounded domains we have to introduce artificial boundaries to confine the computational region. We construct and analyse (discrete) transparent boundary conditions for an implicit difference scheme. We discuss the concepts of positivity and monotonicity of difference schemes and briefly consider these properties of difference schemes for advection–diffusion equations arising in problems of air (and water) pollution. The efficiency and accuracy of our method is illustrated by an example.

Positive Difference Schemes in Neutron Spectral Codes

In the paper a new finite difference scheme assuring positivity of solutions in spectral codes based upon the Greuling-Goertzel approximation is developed. The method can be adopted in any code of ...

Spatial differencing of the transport equation: Positivity vs. accuracy

Positive spatial difference schemes for the Boltzmann equation are derived and compared in x - y geometry. It is found that none of the positive schemes are as accurate as the most commonly used nonpositive scheme. A variable weighted difference scheme in which the weights are chosen depending on the space-angle mesh is shown to give results similar to those obtained with difference schemes based on the method of characteristics. A version of the variable weight scheme in which weights depend not only on the space-angle mesh but also on particle sources and fluxes is suggested as a means of obtaining the highest accuracy consistent with a positive difference scheme, but it is noted that such schemes are computationally more expensive than available corrective recipes used in conjunction with nonpositive schemes.