Peclet Number Behaviour on the 1-D Heat Conduction-Convection Problem with a Control Volume Capacitance Method

Modelling of solidification with transport of mass is of paramount importance for the heat transfer community. Phase change problems have received considerable research attention over the last two decades. Numerical methods for fixed and moving grids have been developed with increasing accuracy and performance, although fundamental aspects still elude modeling such as numerical oscillations. The discovery of Control Volume Capacitance Methods (CVCM) is an attempt to eliminate the need to use classical Petrov-Galerkin and Bubnov-Galerkin formulations. The theory underpinning CVCM methods is presented. A novel modified CVCM is presented which is transformable into a FEM that is similar to that used to model heat-conduction. The method is applied to the 1-D semi-infinite problem, where mesh is spatially fixed whilst mass is transported, in order to investigate the Peclet number behaviour. Numerical tests are compared against analytical solutions; the approach is shown to be accurate, stable and computationally competitive.