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- Publications
- Influence

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

- S. Noelle, Normann Pankratz, G. Puppo, J. Natvig
- Mathematics, Computer Science
- J. Comput. Phys.
- 10 April 2006

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 unperturbed… Expand

Operator spltting methods for systems of convection-diffusion equations: Nonlinear error mechanisms and correction strategies

- K. H. Karlsen, K. Lie, J. Natvig, H. F. Nordhaug, H. Dahle
- Mathematics
- 13 November 2001

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 separate… Expand

Solving the Euler Equations on Graphics Processing Units

- T. Hagen, K. Lie, J. Natvig
- Computer Science
- International Conference on Computational Science
- 28 May 2006

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 dynamics… Expand

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 a… Expand

Flow-based coarsening for multiscale simulation of transport in porous media

- Vera Louise Hauge, K. Lie, J. Natvig
- Computer Science
- Computational Geosciences
- 1 March 2012

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, it… Expand

Visual simulation of shallow-water waves

- T. Hagen, J. M. Hjelmervik, K. Lie, J. Natvig, M. O. Henriksen
- Computer Science
- Simul. Model. Pract. Theory
- 1 November 2005

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 explicit… Expand

Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements

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 time… Expand

Simulation and visualization of the Saint-Venant system using GPUs

- A. Brodtkorb, T. Hagen, K. Lie, J. Natvig
- Mathematics, Computer Science
- Comput. Vis. Sci.
- 1 October 2010

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 graphical… Expand

Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs

- J. Natvig, B. Skaflestad, +4 authors S. Khataniar
- Computer Science
- 2009

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 complex… Expand

A Multiscale Mixed Finite Element Solver for Three Phase Black Oil Flow

- S. Krogstad, K. Lie, H. Nilsen, J. Natvig, B. Skaflestad, J. Aarnes
- Computer Science
- 2009

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 a… Expand