An adaptive numerical method for free surface flows passing rigidly mounted obstacles

TL;DR

This paper introduces an adaptive hybrid finite volume/finite difference numerical method with octree meshes for simulating free-surface flows around rigid obstacles, including offshore oil platforms, demonstrating high accuracy and efficiency.

Contribution

The paper presents a novel adaptive hybrid discretization technique with specialized boundary treatment for simulating complex free-surface flows around submerged structures.

Findings

Accurate simulation of benchmark problems like sloshing and flow past a cylinder.

Successful numerical modeling of flow around an offshore oil platform with realistic data.

Demonstrated effectiveness of adaptive octree meshes in free-surface flow simulations.

Abstract

The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are interested in the paper is a flow around a surface mounted offshore oil platform. The numerical method builds on a hybrid finite volume / finite difference discretization using adaptive octree cubic meshes. The mesh is dynamically refined towards the free surface and the construction. Special care is taken to devise a discretization for the case of curvilinear boundaries and interfaces immersed in the octree Cartesian background computational mesh. To demonstrate the accuracy of the method, we show the results for two benchmark problems: the sloshing 3D container and the channel laminar flow passing the 3D cylinder of circular cross-section. Further, we simulate numerically a flow with surface waves around an offshore oil platform for the realistic set of geophysical data.