Generalized vortex methods for free-surface flow problems

1982 ◽  
Vol 123 ◽  
pp. 477-501 ◽  
Author(s):  
Gregory R. Baker ◽  
Daniel I. Meiron ◽  
Steven A. Orszag
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Bottom Topography ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Three Dimensions ◽  
Fredholm Integral Equations ◽  
Free Surfaces ◽  
Flow Problems ◽  
Dipole Vortex

The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given.

scholarly journals Three-dimensional free-surface flow over arbitrary bottom topography

2018 ◽  
Vol 846 ◽  
pp. 166-189 ◽  
Author(s):  
Nicholas R. Buttle ◽  
Ravindra Pethiyagoda ◽  
Timothy J. Moroney ◽  
Scott W. McCue
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Bottom Topography ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Three Dimensions ◽  
Computational Time ◽  
Algebraic Equations

We consider steady nonlinear free surface flow past an arbitrary bottom topography in three dimensions, concentrating on the shape of the wave pattern that forms on the surface of the fluid. Assuming ideal fluid flow, the problem is formulated using a boundary integral method and discretised to produce a nonlinear system of algebraic equations. The Jacobian of this system is dense due to integrals being evaluated over the entire free surface. To overcome the computational difficulty and large memory requirements, a Jacobian-free Newton–Krylov (JFNK) method is utilised. Using a block-banded approximation of the Jacobian from the linearised system as a preconditioner for the JFNK scheme, we find significant reductions in computational time and memory required for generating numerical solutions. These improvements also allow for a larger number of mesh points over the free surface and the bottom topography. We present a range of numerical solutions for both subcritical and supercritical regimes, and for a variety of bottom configurations. We discuss nonlinear features of the wave patterns as well as their relationship to ship wakes.

Model coupling techniques for free-surface flow problems: Part II

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1897-e1908 ◽  
Author(s):  
E. Miglio ◽  
S. Perotto ◽  
F. Saleri
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Model Coupling ◽  
Flow Problems ◽  
Coupling Techniques

scholarly journals Two infinite-Froude-number cusped free-surface flows due to a submerged line source or sink

1986 ◽  
Vol 28 (2) ◽  
pp. 260-270 ◽  
Author(s):  
I. L. Collings
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Ideal Fluid ◽  
Line Source ◽  
Steady Motion ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Flows ◽  
Flow Problems

AbstractSolutions are found to two cusp-like free-surface flow problems involving the steady motion of an ideal fluid under the infinite-Froude-number approximation. The flow in each case is due to a submerged line source or sink, in the presence of a solid horizontal base.

A weighted Shifted Boundary Method for free surface flow problems

2021 ◽  
Vol 424 ◽  
pp. 109837
Author(s):  
Oriol Colomés ◽  
Alex Main ◽  
Léo Nouveau ◽  
Guglielmo Scovazzi
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Problems ◽  
Boundary Method
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