Nonlinear wave resistance of a two-dimensional pressure patch moving on a free surface

Maki, Kevin J.; Broglia, Riccardo; Doctors, Lawrence J.; Mascio, Andrea Di

doi:10.1016/j.oceaneng.2011.11.003

Cited by 6 publications

(1 citation statement)

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“…Flow past a pressure distribution has been well studied in both an infinitely deep fluid 11,21 or a finite-depth channel. [22][23][24] A variety of variations to this problem have also been considered, such as the inclusion of the effects of surface tension on the free surface 22 or even a layer of mud under the channel. 24 However, for simplicity, we will only consider infinite-depth flows without surface tension or other effects.…”

Section: Flow Past a Pressure Distributionmentioning

confidence: 99%

Efficient computation of two‐dimensional steady free‐surface flows

Pethiyagoda

Moroney

McCue

2017

Numerical Methods in Fluids

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Summary We consider a family of steady free‐surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable techniques, these problems are formulated in terms of a coupled system of Bernoulli equation and an integral equation. When applying a numerical collocation scheme, the Jacobian for the system is dense, as the integral equation forces each of the algebraic equations to depend on each of the unknowns. We present here a strategy for overcoming this challenge, which leads to a numerical scheme that is much more efficient than what is normally used for these types of problems, allowing for many more grid points over the free surface. In particular, we provide a simple recipe for constructing a sparse approximation to the Jacobian that is used as a preconditioner in a Jacobian‐free Newton‐Krylov method for solving the nonlinear system. We use this approach to compute numerical results for a variety of prototype problems including flows past pressure distributions, a surface‐piercing object and bottom topographies.

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