Application of Jacobian-free Newton–Krylov with physics-based preconditioning to biogeochemical transport

Modern multicomponent geochemical transport models require the use of parallel computation for carrying out three-dimensional, field-scale simulations due to extreme memory and processing demands. However, to fully exploit the advanced computational power provided by today’s supercomputers, innovative parallel algorithms are needed. We demonstrate the use of Jacobian-free Newton–Krylov (JFNK) within the Newton–Raphson method to reduce memory and processing requirements on high-performance computers. We also demonstrate the use of physics-based preconditioners, which are often necessary when using JFNK since no explicit Jacobian matrix is ever formed. We apply JFNK to simulate enhanced in situ bioremediation of a NAPL source zone, which entails highly coupled geochemical and biodegradation reactions. The algorithm’s performance is evaluated and compared with conventional solvers and preconditioners. We found that JFNK provided substantial saving in memory (i.e. 30–60%) on problems utilizing up to 512 processors on LANL’s ASCI Q. However, the performance based on wallclock time was less advantageous, coming out on par with conventional techniques. In addition, we illustrate deficiencies in physics-based preconditioner performance for biogeochemical transport problems with components that undergo significant sorption or form a local quasi-stationary state.