Universal parallel numerical computing for 3D convection-diffusion equation with variable coefficients

A universal parallelized numerical approach for solving the three-dimensional (3D) convection diffusion equation with variable coefficients is proposed by combining the implicit difference method of Crank-Nicolson with alternating bar parallelization, which can be used to solve numerically any variation of the 3D convection diffusion equation. By virtue of bar parallelization and a multistep iteration technique, this approach trades off parallelism and accuracy. Its main merits are generality, absolute stability, acceptable space requirements and second-order accuracy. Its parallel implementation, named Codie4D, on a network of workstations using the MPI library uses the benefits of portability and applicability. Experimental results show that Codie4D has good runtime performance.