Towards Simulation of Complex Ocean Flows: Analysis and Algorithm for Computation of Coupled Partial Differential Equations

Author

Wenbin Dong, CUNY City CollegeFollow

Date of Award

2022

Document Type

Dissertation

Department

Civil Engineering

First Advisor

Hansong Tang

Keywords

CFD, Schwarz iteration, interface treatment, hybrid model

Abstract

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass or momentum across the interface. Even several different prototypes of interface treatments have been reported but have not been tested on 3D problems or coupling different sets of PDEs. In this thesis, a systemic study about the overlapping domain decomposed problem is presented into the 3 following aspects:

1. Convergence analysis

Towards a rigorous mathematical foundation, a study of 1D domain decomposed problem based on advection-diffusion-reaction equation is made. Both Schwarz-Time process and Time-Schwarz process have been analysed with a new but simple method called fully discretization analysis. The convergence ratio formulas of classic and optimized interface treatments have been formed. The expressions for the optimized coefficient pair are found for some cases.

2. Accurate interface algorithm

The back and forth error compensation and correction method(BFECC), an accuracy-enhancement method is applied with the interpolation scheme. A fully investigation is made for it, such as supercovnergence, interpolation scheme, node density, mesh ratio, mesh rotation, and mesh with perturbation. Case study on 3D domain decomposed simulation with same sub-model is done, the results generated by different interface treatments show that the calculation benefits from higher order treatment.

3. Different interface treatments

The example hybrid CFD model(SIFOM-FVCOM) is studied with the governing equations, grid types, numerical schemes, and calculation flows. The numerical experiments are made by applying different interface treatments on SIFOM-FVCOM. The differences of the results indicate that the interface treatment play a crucial role in success of such simulations. \end{enumerate}

This work improves the understanding of the grounded mathematical problem, the effectiveness of optimized interface treatment, the importance of interface treatment's accuracy, and the otherness of applying different interface treatments. In addition, it advances our capability in further developing the interface treatment with better convergence rate as well as higher fidelity.

Recommended Citation

Dong, Wenbin, "Towards Simulation of Complex Ocean Flows: Analysis and Algorithm for Computation of Coupled Partial Differential Equations" (2022). CUNY Academic Works.
https://academicworks.cuny.edu/cc_etds_theses/1072