| Title | Exponential Euler Time Integrator for Simulation of Geothermal Processes in Heterogeneous Media |
|---|---|
| Authors | Antoine TAMBUE, Inga BERRE, Jan NORDBOTTEN, Tor Harald SANDVE |
| Year | 2012 |
| Conference | Stanford Geothermal Workshop |
| Keywords | geothermal processes, exponential integrator, Krylov subspace , fast time integrators |
| Abstract | 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. |