The multiscale structure of heterogeneous porous media prevents a straightforward numerical treatment of the underlying mathematical ow models. In particular, fully resolved ow simulations are intractable and yet the ne-scale structure of a porous medium may signiicantly innuence the coarse-scale properties of the solution (e.g., average ow rates). Consequently, homogenization or upscaling proc...

We compare various preconditioners for the numerical solution of partial differential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is always, i.e. for all deflation vectors and all restrictions and prolongations, belo...

We consider numerical solutions of the Darcy and Buckley-Leverett equations for ow in porous media. These solutions depend on the geology of the porous media, which is given here as a realization of a random eld to describe the reservoir permeability. We measure the solution error as the diierence between the oil production rates (oil cut) for ne grid and upscaled coarse grid solutions of the e...

Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable long term simulations. This is typically done via parametrizations but their coupling to the coarse grid variables often involves simple heuristics. We explo...

in this paper wave transformation in a submerged sloped breakwater and its hydraulic performance was simulated by developing a numerical model in fortran. the code was established by combining porous flow and a two-phase model using vof method. modified navier-stokes and k-ε equations implemented to the model to simulate the flow in porous media. cut cell method was modified to simulate fluid t...

We consider additive Schwarz domain decomposition preconditioners for piecewise linear finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to standard analyses, we do not assume that the coefficients can be resolved by a coarse mesh. This situation arises often in practice, for example in the computation of flows in heterogeneous porous media, in both t...