Robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids

Streamline methods for subsurface-flow simulation have received renewed attention as fast alternatives to traditional finite volume or finite element methods. Key aspects of streamline simulation are the accurate tracing of streamlines and the computation of travel time along individual streamlines. In this paper, we propose a new streamline tracing framework that enables the extension of streamline methods to unstructured grids composed of triangular or quadrilateral elements and populated with heterogeneous full-tensor coefficients. The proposed method is based on the mathematical framework of mixed finite element methods, which provides approximations of the velocity field that are especially suitable for streamline tracing. We identify and implement two classes of velocity spaces: the lowest-order Raviart–Thomas space (low-order tracing) and the Brezzi–Douglas–Marini space of order one (high-order tracing), both on triangles and quadrilaterals. We discuss the implementation of the streamline tracing method in detail, and we investigate the performance of the proposed tracing strategy by means of carefully designed test cases. We conclude that, for the same computational cost, high-order tracing is more accurate (smaller error in the time-of-flight) and robust (less sensitive to grid distortion) than low-order tracing.