Anderson Acceleration for Maritime Applications

In general, most of the computational effort required to do numerical simulations for maritime applications is spent to solve systems of non-linear equations. For time-dependent simulations such systems have to be solved every time step, and to be sure a correct time-dependent behavior is simulated, the time step cannot be chosen too large. To ensure that the accuracy of the simulations is not spoiled by grid dependence, sufficiently fine meshes have to be used, which causes these systems to become large. Therefore, in Ploeg, 2019 we studied the effectiveness of an acceleration strategy introduced in Anderson, 1965 to reduce the computational effort. In the sequel of this report, this strategy will be referred to as Anderson Acceleration (AA).
In Ploeg, 2019 is was shown that AA can significantly speed up the solution of the systems of nonlinear equations as they occur in the computation of incompressible flows. Especially for 2D problems without turbulence, the improvement in convergence rate can be spectacular and a reduction in the required wall clock time of more than one order of magnitude can be obtained. However, for more realistic 3D test cases with turbulence, with meshes suited to resolve boundary layers, the reduction of the wall clock time was not as spectacular. Typically, a reduction of only 30% could be achieved. Moreover, the solution of the minimization problem required by the AA algorithm was not yet parallelized. In this paper, we address these issues.We will describe a parallelizable algorithm of AA including a proper scaling that improves the convergence also for realistic 3D cases.