Analytic Coarse-Mesh Finite-Difference Method Generalized for Heterogeneous Multidimensional Two-Group Diffusion Calculations

Convergence Analysis of the Nonlinear Coarse Mesh Finite Difference Method

The convergence rates for the non-linear coarse mesh finite difference (CMFD) method and the coarse mesh rebalance (CMR) method are derived analytically for one-group, one-dimensional solutions of the fixed source diffusion problem in a non-multiplying infinite homogeneous medium. The derivation was performed by linearizing the non-linear algorithm and by applying Fourier error analysis to the ...

A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

A Three Dimensional Heterogeneous Coarse Mesh Transport Method for Reactor Calculations

Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues.

We analyse the limits of the diffusion approximation to the time-independent equation of radiative transfer for homogeneous and heterogeneous biological media. Analytical calculations and finite-difference simulations based on diffusion theory are compared with discrete-ordinate, finite-difference transport calculations. The influence of the ratio of absorption and transport scattering coeffici...

Moving Mesh Non-standard Finite Difference Method for Non-linear Heat Transfer in a Thin Finite Rod

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...