High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner

Highlights: • Two techniques to speedup large scale simulations of viscous fingering using implicit DG are presented. • The first technique relies on a simple p-adaptive scheme and results in significant reduction in the problem size. • In the second technique, we design an algebraic multigrid (AMG) to improve the solver efficiency. • The new techniques enable high resolution 3D viscous fingering simulations in greater detail than before. High resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena. The fully implicit discontinuous Galerkin (DG) method has been shown to be an accurate and stable method to model viscous fingering with high Peclet number and mobility ratio. In this paper, we present two techniques to speedup large scale simulations of this kind. The first technique relies on a simple p-adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change. As a result, the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh. The second technique for speedup involves improving the solver efficiency. We present an algebraic multigrid (AMG) preconditioner which allows the DG matrix to leverage the robust AMG preconditioner designed for the continuous Galerkin (CG) finite element method. The resulting preconditioner works effectively for fixed order DG as well as p-adaptive DG problems. With the improvements provided by the p-adaptivity and AMG preconditioning, we can perform high resolution three-dimensional viscous fingering simulations required for miscible displacement with high Peclet number and mobility ratio in greater detail than before for well injection problems.