[M-IS12] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS12-P04] An explicit time integration technique for incompressible permeable fluid flow using the reduced sound speed method: Solving a slow flow problem fast, Part 2

*Yoshifumi Kawada¹ (1.Japan Agency for Marine-Earth Science and Technology)

Keywords:permeable flow, hydrothermal circulation, explicit method

We propose an efficient explicit method for calculating permeable fluid flow using the reduced sound speed method combined by the large timestep Renge-Kutta method. This technique was originally developed to solve the nearly-incompressible Navier-Stokes equation explicitly; the remarkable characteristic of this method is its simplicity in implementation. Here, we adapt the method to permeable flow. The compressibility of pore fluid is small, and the sound speed is fast. Thus, a simple explicit time integration requires a very small time step for fluids with small compressibility. In such cases, an implicit or iterative time integration must be used for efficiency. Another method, taking infinite sound speed, i.e., the incompressible approximation, makes the system simple. However, this requires solving the Poisson equation for pressure, which also requires iterations. In contrast, our implementation of the reduced sound speed method for permeable flow can solve this system explicitly, i.e., no iteration is required.
We solve a thermal convection problem in a closed box heated from below using the proposed explicit method as well as a conventional iterative method with the multigrid method. We compare the results for both methods and find that they agree very well. Additionally, we examine the CPU time required for the calculation of these methods. We find that the efficiency of our explicit method is nearly comparable to that of the implicit method. This indicates that our method has advantages for applying to large-scale parallel computations. Furthermore, this simple method is convenient for a platform for testing new ideas.