This project provides simple code for solving the stationary transport equation for a scalar quantity in a given fluid flow a uniform grid. In the problem cases this scalar quantity is the dimensionless temperature. Therefore the problem only depends upon the Peclét number, Pe which is a ratio betweem convection and diffusion. The fluxes used in the finite volume scheme are approximated by finite differences: For the diffusive part of the equation, the central difference scheme, CDS are always applied since diffusion acts in all directions independent of the flow. For the convective part, either CDS or upwind difference scheme, UDS is applied. UDS only used infomation from the upstream direction. CDS is second order, whereas UDS only is first-order. Combining CDS-CDS results in oscillations and divergence on coarser grids (Pe*dx>2), but generally gives a more accurate solution than CDS-UDS. The CDS-UDS scheme always result in a diagonal-dominant system matrix, which should be the case the numerical method should mimic the physics. CDS-UDS should not be used since it reduce the order of the finite volume method.

FVConvDiff2D.preprocess.py: Assembles system matrix and source vector.

FVConvDiff2D.postprocess.py: Extrapolates field to domain borders and checks global flux error.

UniformFlow.py: Solves for a uniform cavity flow problem and visualizes the results.

StagnationPointFlow.py: Solves for a stagnation point cavity flow problem and visualizes the results.

ConvergenceTo1dUniformFlowSolution.py: Checks the convegence of the different combinations for the uniform flow problem.

OptimalSOR.py: Find optimal relaxation factors for both problems using various grid sizes and Peclét numbers.

SIMPy.py: Basic stationary iterative solvers for sparse matrix systems in python.