Sammendrag
Higher-order methods have only been applied to a limited extent in simulation of real petroleum assets. Possible reasons are complex grid formats (unstructured, polyhedral cells, large aspect ratios) and need for implicit time discretization. I this talk, we outline how weighted essentially non-oscillating (WENO) methods and discontinuous Galerkin (dG) methods can be adapted to the needs of reservoir simulation. We discuss some implementation details and highlight advantages and shortcomings of the two methods on a number of test cases, including models representing real reservoirs.