High Order Boundary Integral Methods for Viscous Free Surface Flows

1994 ◽  
pp. 49-66 ◽  
Author(s):  
J. J. L. Higdon ◽  
C. A. Schnepper
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
High Order ◽  
Surface Flows ◽  
Boundary Integral Methods ◽  
Integral Methods

A B-Spline Based BEM for Unsteady Free-Surface Flows

1999 ◽  
Vol 43 (01) ◽  
pp. 13-24
Author(s):  
M. Landrini ◽  
G. Grytøyr ◽  
O. M. Faltinsen
Keyword(s):  
Free Surface ◽  
Evolution Equations ◽  
Boundary Integral Equations ◽  
Fluid Dynamic ◽  
Domain Boundary ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Surface Flows ◽  
B Spline ◽  
Nonlinear Free Surface

Fully nonlinear free-surface flows are numerically studied in the framework of the potential theory. The problem is formulated in terms of boundary integral equations which are solved by means of an arbitrary high-order boundary element method based on B-Spline representation of both the geometry and the fluid dynamic variables along the domain boundary. The solution is stepped forward in time either by following Lagrangian points attached to the free surface or by a less conventional scheme in which evolution equations for the B-Spline coefficients are integrated in time. Numerical examples for inner and outer free-surface flows are shown. The accuracy of the numerical solution is assessed either by checking mass and energy conservation or by comparing with reference solutions. Good results are generally obtained. Extended use of the developed algorithm to more applied problems in the context of naval hydrodynamics is now under development.

Free-surface flows past a surface-piercing object of finite length

1994 ◽  
Vol 273 ◽  
pp. 109-124 ◽  
Author(s):  
J. Asavanant ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Three Solutions ◽  
Surface Flows ◽  
Sharp Crest ◽  
Supercritical Flows

Steady two-dimensional flows past a parabolic obstacle lying on the free surface in water of finite depth are considered. The fluid is treated as inviscid and incompressible and the flow is assumed to be irrotational. Gravity is included in the free-surface condition. The problem is solved numerically by using boundary integral equation techniques. It is shown that there are solutions for which the flow is supercritical both upstream and downstream and others for which the flow is subcritical both upstream and downstream. These flows have continuous tangents at both ends of the obstacle at which separation occurs. For supercritical flows, there are up to three solutions corresponding to the same value of the Froude number when the obstacle is concave and up to two solutions when the obstacle is convex. For subcritical flows, there are solutions with waves behind the obstacle. As the Froude number decreases, these waves become steeper and the numerical calculations suggest that they, ultimately, reach limiting configurations with a sharp crest forming a 120° angle.

scholarly journals A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

2020 ◽  
Author(s):  
Matteo Bergami ◽  
Walter Boscheri ◽  
Giacomo Dimarco
Keyword(s):  
Free Surface ◽  
Sediment Transport ◽  
Numerical Scheme ◽  
Control Volume ◽  
Free Surface Flows ◽  
High Order ◽  
Time Step ◽  
Reconstruction Procedure ◽  
Surface Flows ◽  
Lagrangian Scheme

AbstractIn this paper, we present a conservative semi-Lagrangian scheme designed for the numerical solution of 3D hydrostatic free surface flows involving sediment transport on unstructured Voronoi meshes. A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume. This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms. The presented method is fully conservative by construction, since the transported quantity or the vector field is integrated for each cell over the deformed volume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element. The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations. Furthermore, a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance, hence yielding a stability condition which depends only on the explicit discretization of the viscous terms. A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment, which is assumed to be passive. The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solution whenever is known. The new numerical scheme can reach up to fourth order of accuracy on general orthogonal meshes composed by Voronoi polygons.

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