Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition

We propose a space-time finite volume scheme on moving Chimera grids for general advection-diffusion problem. Special care is devoted to grid overlapping zones in order devise compact and accurate discretization stencil exchange information between different mesh patches. Like the arbitrary high derivatives method, equations are discretized slab. Thus, instead of time-dependent spatial transmission conditions relatively blocks, we define interpolation polynomials arbitrarily intersecting cells at block boundaries. Through this scheme, mesh-free FEM-predictor/FVM-corrector approach employed representing solution. In framework, new local Lax--Friederichs stabilization speed defined by considering both advective diffusive nature equation. The numerical illustrations linear nonlinear systems show that background foreground meshes do not introduce spurious perturbation solution, uniformly reaching second accuracy space time. Finally, it shown several meshes, possibly with independent displacements, can be thanks approach.