Efficient computation of steady, 3D water-wave patterns

Numerical methods for the computation of stationary free surfaces is the subject of much current research in computational engineering. The present report is directed towards free surfaces in maritime engineering. Of interest here are the long steady waves generated by ships, the gravity waves. In the present report an existing 2D iterative method for the computation of stationary gravity-wave solutions is extended to 3D, numerically investigated, and improved. The method employs the so-called quasi free-surface boudary condition. As test cases we cosider gravity-wave patterns due to pressure perturbations imposed at the free surface of a steady, uniform horizontal flow. The effects are studied of the distance of the imposed pressure distribution to the far-field boundary, the magnitude of the imposed pressure perturbation, and the mesh widths. In all experiments, our focus is on the convergence behavior of the free-surface iteration process

Efficient computation of steady, 3D water-wave patterns, application to hovercraft-type flows

Numerical methods for the computation of stationary free surfaces is the subject of much current research in computational engineering. The present report is directed towards free surfaces in maritime engineering. Of interest here are the long steady waves generated by hovercraft and ships, the gravity waves. In the present report an existing 2D iterative method for the computation of stationary gravity-wave solutions is extended to 3D, numerically investigated, and improved. The method employs the so-called quasi free-surface boundary condition. As test cases we consider gravity-wave patterns due to hovercraft-type pressure perturbations imposed at the free surface of a steady, uniform horizontal flow. The effects are studied of the distance of the imposed pressure distribution to the far-field boundary, the magnitude of the imposed pressure perturbation, the mesh widths, as well as the presence of a no-slip boundary intersecting the free surface. In all experiments, our focus is on the convergence behavior of the free-surface iteration process

Riemann-problem and level-set approaches for two-fluid flow computations II. Fixes for solution errors near interfaces.

Fixes are presented for the solution errors (`pressure oscillations') that may occur near two-fluid interfaces when applying a capturing method. The fixes are analyzed and tested. For two-fluid flows with arbitrarily large density ratios, a variant of the ghost-fluid method appears to be a perfect remedy. Results are presented for compressible water-air flows. The results are promising for a further elaboration of this important application area. The paper contributes to the state-of-the-art in computing two-fluid flows

Riemann-problem and level-set approaches for homentropic two-fluid flow computations

A finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. A novel ingredient in the method is a linearized, two-fluid Osher scheme, allowing for flux computations in the case of different fluids (e.g., water and air) left and right of a cell face. A level-set technique is employed to distinguish between the two fluids. The level-set equation is incorporated into the system of hyperbolic conservation laws. Fixes are presented for the solution errors (pressure oscillations) that may occur near two-fluid interfaces when applying a capturing method. The fixes are analyzed and tested. For two-fluid flows with arbitrarily large density ratios, a simple variant of the ghost-fluid method appears to be a perfect remedy. Computations for compressible water–air flows yield perfectly sharp, pressure-oscillation-free interfaces. The masses of the separate fluids appear to be conserved up to first-order accuracy

An Osher-type and level-set scheme for two-fluid flow computations

A simple and efficient finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. One novel ingredient in the method is a two-fluid Osher-type scheme, which is capable of computing the cell-face flux in case of two different fluids (e.g., water and air) left and right of the cell face. The other original property of the method is that a level-set term, for distinguishing between the two fluid8, is consistently incorporated as one of the flux components. The level-set flux is properly treated by the Osher-type scheme

An efficient numerical method for 3D viscous ship hydrodynamics with free-surface gravity waves

A new numerical method for water flows with free-surface gravity waves is investigated. The method is first analyzed with respect to the existence of steady free-surface waves, and the dispersion properties of these waves. Next, the method is used to compute the free water surface generated by a standard ship hull

An efficient numerical method for 3D viscous ship hydrodynamics with free-surface gravity waves

A new numerical method for water flows with free-surface gravity waves is investigated. The method is first analyzed with respect to the existence of steady free-surface waves, and the dispersion properties of these waves. Next, the method is used to compute the free water surface generated by a standard ship hull