Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Euler time integrator with finite volume (two-point or multi-point flux approximations) space discretizations leads to a robust methodology for simulating geothermal systems. In terms of efficiency and accuracy, the exponential Euler time integrator has advantages over standard time-dicretization schemes, which suffer from time-step restrictions or excessive numerical diffusion when advection processes are dominating. Based on linearization of the equation at each time step, we make use of a matrix exponential function of the Jacobian, which then provides the exact solution in time for the linearized equations. This is at the expense of computing a matrix exponential function of the stiff Jacobian matrix from the space discretization, together with propagating a linearized system. However, using a Krylov subspace technique makes this computation very efficient, and it can also be implemented without explicit computation of the Jacobian. At the same time, the loss of accuracy due to the linearization does not dominate for geothermal processes. The performance of the method compared to standard time-discretization techniques is demonstrated in numerical examples.

Press the Back button in your browser, or search again.

Copyright 2012, Stanford Geothermal Program: Readers who download papers from this site should honor the copyright of the original authors and may not copy or distribute the work further without the permission of the original publisher.