Efficient solution techniques for two-phase flow in heterogeneous porous media using exact Jacobians
| Autor: | Büsing, Henrik, Institute for Applied Geophysics and Geothermal Energy, E.ON Energy Research Center, RWTH Aachen University, Aachen, Germany |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Discretization
Automatic differentiation Computer science Schur complement reduction (SCR-AMG) 76T10 65F08 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Newton's method in optimization symbols.namesake Multigrid method 020401 chemical engineering ddc:550 Applied mathematics 0204 chemical engineering 0101 mathematics Computers in Earth Sciences Constrained pressure residual (CPR-AMG) Multiphase flow in porous media 65M55 Linear system Finite difference Computer Science Applications Automatic differentiation (AD) Computational Mathematics Computational Theory and Mathematics Jacobian matrix and determinant symbols Schur complement CO2 geo-sequestration ddc:550.2 Algebraic multigrid (AMG) |
| Zdroj: | Computational geosciences 25(1), 163-177 (2020). doi:10.1007/s10596-020-09995-w |
| Popis: | Two efficient and scalable numerical solution methods will be compared using exact Jacobians to solve the fully coupled Newton systems arising during fully implicit discretization of the equations for two-phase flow in porous media. These methods use algebraic multigrid (AMG) to solve the linear systems in every Newton step. The algebraic multigrid methods rely on (i) a Schur Complement Reduction (SCR-AMG) and (ii) a Constrained Pressure Residual method (CPR-AMG) to decouple elliptic and hyperbolic contributions. Both methods employ automatic differentiation (AD) to calculate exact Jacobians and are compared with finite difference (FD) approximations of the Jacobian. The superiority of AD is shown by several numerical test cases from the field of CO2 geo-sequestration comprising two- and three-dimensional examples. A weak scaling test on JUQUEEN, a BlueGene/Q supercomputer, demonstrates the efficiency and scalability of both methods. To achieve maximum comparability and reproducibility, the Portable Extensible Toolkit for Scientific Computation (PETSc) is used as framework for the comparison of all solvers. Horizon 2020 https://doi.org/10.13039/501100007601 |
| Databáze: | OpenAIRE |
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