Moving elements for reservoir transport processes

The authors consider a class of convection-dominated flows fundamental to reservoir simulation, and their approximate solution using finite element techniques and moving meshes. Both the solution field and the coordinate functions enter as primary unknowns in the resulting problem statement. Hence the mesh evolves with the solution, and the method is particularly well-suited to those problems in which tracking of sharp solution fronts is important. Examples of particular interest related to petroleum reservoir simulation are the model convection diffusion, Burgers', and Buckley Leverett equations, which are considered in the numerical studies. They consider effective solution techniques and system integration, as well as questions related to the use of constraints for limiting the permissible distortion of the mesh.