Adaptive mesh refinement for compressible thermal flow in porous media

We present the implementation of a detailed model for compositional flow in porous media into an adaptive mesh refinement (AMR) framework. This model is applicable to a number of thermal problems. The basic numerical approach is an efficient shock-capturing method designed to minimise the number of expensive phase equilibrium calculations needed per time step. This is implemented in an AMR framework, using a multigrid method for general parabolic equations. The AMR method is applicable to a general class of hyperbolic-parabolic problems which includes the porous media model. We test the method on one-dimensional and two-dimensional thermal gas injection test cases, including non-uniform propagation in a heterogeneous medium.