Numerical Approximation of a Transport Equation with a Time‐Dependent Dispersion Flux

Cidália Neves, Adérito Araújo, Ercília Sousa
The objective of this work is to discuss a more general one-dimensional diffusion equation that accounts for certain aspects such as the variation of a parameter that describes the relaxation time of the mass flux and also the presence of a potential field. The equation will have properties similar to a an hyperbolic equation or parabolic equation according to which values of the relaxation parameter or the potential field we consider. In the hyperbolic case we deal with some discontinuities.
more » ... discontinuities. We apply a numerical scheme to solve this equation, which consists of using an inverse Laplace transform algorithm. The Laplace method is used to remove the time-dependent terms in the governing equation and boundary conditions. For a constant potential field general solutions can be determined. On the other hand for a non-constant potential field, a spatial discretisation must be considered. We will study the convergence of the numerical scheme based on the inverse of Laplace transform and present some test problems.
doi:10.1063/1.2990947 fatcat:3i52nlkybvb6fax3ivogso2ze4