Nonlinear reaction-convection-diffusion equations are encountered in
modeling of a variety of natural phenomena such as in chemical reactions,
population dynamics and contaminant dispersal. When the
scale of convective and reactive phenomena are large, Galerkin finite
element solution fails.
As a remedy, Orthogonal Subgrid Scale stabilization is applied to the
finite element formulation. It has its origins in the Variational Multi
Scale approach. It is based on a fine grid - coarse grid component sum
decomposition of solution and utilizes the fine grid solution orthogonal
to the residual of the finite element coarse grid solution as a correction
term. With selective mesh refinement, a stabilized oscillation-free
solution that can capture sharp layers is obtained. Newton Raphson
method is utilized for the linearization of nonlinear reaction terms.
Backward difference scheme is used for time integration.
The formulation is tested for cases with standalone and coupled systems
of transient nonlinear reaction-convection-diffusion equations.
Method of manufactured solution is used to test for correctness and
bug-free implementation of the formulation. In the error analysis,
optimal convergence is achieved. Applications in channel flow, cavity
flow and predator-prey model is used to highlight the need and
effectiveness of the stabilization technique.
