High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs
We consider high order, implicit Runge Kutta schemes to solve time dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume scheme yields highly compressed representations within a user defined accuracy tolerance, hence strong reductions of computational requirements to solve large, coupled nonlinear systems of equations. SDIRK and RadauIIA Runge Kutta schemes are implemented with particular interest in those with L stability properties and accuracy based time stepping capabilities. Numerical evidence is provided of the computational efficiency of the numerical strategy to cope with highly unsteady problems modeling various physical scenarios with a broad spectrum of time and space scales.