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Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbedExpand
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Operator spltting methods for systems of convection-diffusion equations: Nonlinear error mechanisms and correction strategies
Abstract Many numerical methods for systems of convection–diffusion equations are based on an operator splitting formulation, where convective and diffusive forces are accounted for in separateExpand
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Solving the Euler Equations on Graphics Processing Units
The paper describes how one can use commodity graphics cards (GPUs) as a high-performance parallel computer to simulate the dynamics of ideal gases in two and three spatial dimensions. The dynamicsExpand
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An efficient discontinuous Galerkin method for advective transport in porous media
We consider a discontinuous Galerkin scheme for computing transport in heterogeneous media. An efficient solution of the resulting linear system of equations is possible by taking advantage of aExpand
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Flow-based coarsening for multiscale simulation of transport in porous media
Geological models are becoming increasingly large and detailed to account for heterogeneous structures on different spatial scales. To obtain simulation models that are computationally tractable, itExpand
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Visual simulation of shallow-water waves
A commodity-type graphics card (GPU) is used to simulate nonlinear water waves described by a system of balance laws called the shallow-water system. To solve this hyperbolic system we use explicitExpand
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Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements
  • J. Natvig, K. Lie
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 30 December 2008
We present a family of implicit discontinuous Galerkin schemes for purely advective multiphase flow in porous media in the absence of gravity and capillary forces. To advance the solution one timeExpand
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Simulation and visualization of the Saint-Venant system using GPUs
We consider three high-resolution schemes for computing shallow-water waves as described by the Saint-Venant system and discuss how to develop highly efficient implementations using graphicalExpand
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Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs
Advances in reservoir characterization and modeling have given the industry improved ability to build detailed geological models of petroleum reservoirs. These models are characterized by complexExpand
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A Multiscale Mixed Finite Element Solver for Three Phase Black Oil Flow
Previous research has shown that multiscale methods are robust and capable of providing more accurate solutions than traditional upscaling methods. Multiscale methods solve the pressure equation on aExpand
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