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

Journal of Computational Physics

Becker, G.; Siefert, C.M.; Tuminaro, Raymond S.; Sun, H.; Valiveti, D.M.; Mohan, A.; Yin, J.; Huang, H.

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.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

An algebraic multigrid method for Q2−Q1 mixed discretizations of the Navier–Stokes equations

Numerical Linear Algebra with Applications

Prokopenko, Andrey V.; Tuminaro, Raymond S.

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily colocated at mesh points. Specifically, we investigate a Q2−Q1 mixed finite element discretization of the incompressible Navier–Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees of freedom (DOFs) are defined at spatial locations where there are no corresponding pressure DOFs. Thus, AMG approaches leveraging this colocated structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocity DOF relationships of the Q2−Q1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity DOFs resembles that on the finest grid. To define coefficients within the intergrid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier–Stokes problems.

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TYPE Journal Article YEAR 2017
ScopusOSTIDOI
Results 26–50 of 170
Results 26–50 of 170