Boundary Integral Eqution Formulation for Free Surface Flow Problems in Two and Three Dimensions

1988 ◽  
pp. 359-367 ◽  
Author(s):  
J. E. Romate ◽  
P. J. Zandbergen
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Flow Problems

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
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