A spectral multidomain penalty method model for the simulation of internal solitary wave shoaling and breaking over gentle slopes

This presentation outlines the basic components of an MPI-parallelized high-accuracy/resolution fully nonlinear and non-hydrostatic spectral multidomain penalty method solver designed to simulate the shoaling and potential breaking of internal solitary waves (ISWs) over long distances along gentle slopes. The solver employs deformed quadrilateral 2-D Legendre-polynomial based subdomains in the along-wave propagation direction. A Fourier discretization in the transverse direction, allows for the simulation of turbulence under the assumption that ISWs propagate normal to the isobaths, as is the case in the South China Sea (SCS). The use of high-order element-based techniques minimizes spurious dissipation/mixing at the smallest-resolved scales, enables wave propagation over long distances free of numerical dispersion and permits flexibility in resolving localized dynamics within an ISW.

Particular emphasis is placed on an efficient pressure Poisson equation (PPE) solver designed to efficiently capture the strongly non-hydrostatic dynamics of shoaling ISWs on highly leptic grids. To minimize the number of iterations in the PPE solver, an iterative substructuring approach is employed to assemble and solve the Schur problem of the Poisson matrix. For high-order methods, this Schur problem is far smaller and better conditioned than the original operator. Then, a block-diagonal preconditioner is used to mitigate the effects of domain aspect ratio, and a deflation technique bounds the number of GMRES iterations required in the iterative solution as the number of subdomains grows. The performance and accuracy of the preconditioned iterative substructuring are evaluated as is also the scalability of these methods in a practical distributed parallel computing environment.

The remaining numerical discussion focuses on validation of the code through specific ISW-based flow benchmarks. Select results will be shown for ISWs shoaling over actual SCS bathymetry with realistic background stratification and currents. Some first 3-D snapshots of the transition of turbulence in a convectively breaking wave will be shown. Finally, preliminary results on Lagrangian particle tracking in the associated trapped cores will be presented.