Parallel Newton-Krylov solvers for modeling of a navigation lock filling system

Abstract

The Galerkin least-squares finite element method for solving the Reynolds-averaged incompressible turbulent 3-D Navier-Stokes equations is employed to simulate a navigation lock filling system in the numerical code Adaptive Hydraulics (ADH). The linear system is solved at each nonlinear iteration within every time-step using biconjugate gradient stabilized (BiCGstab) in combination with block-Jacobi (bjacobi) preconditioners, as it failed to solve the linear system because of dramatic changes in flow velocity and pressure early in the simulation. To overcome this problem, we used the Portable Extensible Toolkit for Scientific Computation (PETSc), a numerical library that provides multiple types of linear solvers. PETSc has been incorporated into the ADH code. The ADH-PETSc interface helps to systematically investigate the best linear solver for an ADH simulation. We found that a variant, known as enhanced BiCGstab(l) in combination with the additive Schwarz method (ASM), made it possible to simulate the John Day lock filling system. The BiCGstab(l) solver improved the rate of convergence because of a more reliable update strategy for the residuals. In addition, the simulation was run with various numbers of processors. The result shows good scaling of solution time as the number of processors increases