A time-splitting method on a nonstaggered grid in curvilinear coordinates for implicit simulation of non-hydrostatic free-surface flows

2007 ◽  
Vol 34 (1) ◽  
pp. 99-106 ◽  
Author(s):  
M Javan ◽  
M M Namin ◽  
S A.A. Salehi Neyshabouri
Keyword(s):  
Free Surface ◽  
Moving Boundary ◽  
Control Volume ◽  
Splitting Method ◽  
Free Surface Flows ◽  
Curvilinear Coordinates ◽  
Surface Boundary ◽  
Surface Flows ◽  
Free Surface Boundary Condition ◽  
Time Splitting

The numerical solution of flows with a freely moving boundary is of great importance in practical application such as ship hydrodynamics. Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady and steady free-surface flows on a nonstaggered grid in curvilinear coordinates, using a non-hydrostatic pressure distribution. In this model, Reynolds equation and the kinematic free-surface boundary condition are solved simultaneously, so that the water-surface elevation can be integrated into the solution and solved for, together with the velocity and pressure field. In computational space, the Cartesian velocity components and the pressure are defined at the center of a control volume, while the volume fluxes are defined at the midpoint on their corresponding cell faces. Detailed numerical results are presented for the wave generation above an obstacle and resonant motion standing wave. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.Key words: free-surface simulation, nonstaggered grid, time-splitting method, unsteady flow, turbulent flow.

Properties of Finite-Difference Operators for the Steady-Wave Problem

1993 ◽  
Vol 37 (01) ◽  
pp. 1-7
Author(s):  
John S. Letcher
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Radiation Condition ◽  
Free Surface Flows ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Difference Operators ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A feature of most implementations of Dawson's boundary-integral method for steady free-surface flows is the use of upstream finite-difference operators for the streamwise derivative occurring in the linearized free-surface boundary condition. An algebraic analysis of a family of candidate operators reveals their essential damping and dispersion error characteristics, which correlate well with their observed performance in two-dimensional example flows. Some new operators are found which perform somewhat better than Dawson's, but the general outlook for accurate results using difference operators is nevertheless bleak. It is shown that the calculation necessarily diverges as panel size is reduced, and a breakdown at higher speeds is also inevitable. More promise appears to lie in satisfying the radiation condition by several alternative ways, which are briefly discussed.

A geometric approach to the study of stationary free surface flows for viscous liquids

1993 ◽  
Vol 123 (2) ◽  
pp. 209-229 ◽  
Author(s):  
Frédéric Abergel
Keyword(s):  
Free Surface ◽  
Simple Structure ◽  
Space Dimension ◽  
Geometric Approach ◽  
Free Surface Flows ◽  
Surface Boundary ◽  
Surface Flows ◽  
Viscous Liquids ◽  
Stationary Flows ◽  
Surface Boundary Conditions

SynopsisWe use a direct, geometric approach to study the free surface boundary conditions for stationary flows of viscous liquids. The free surface problem is characterised by a mapping on smooth variations of a given configuration; this mapping has a simple structure, which we determine by computing its differential, and studying it in terms of the space dimension and the surface tension coefficient. Applications are given to problems of existence, uniqueness and regularity in free surface flows.

scholarly journals A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

2018 ◽  
Vol 172 ◽  
pp. 384-396
Author(s):  
Sébastien Boyaval ◽  
Alexandre Caboussat ◽  
Arwa Mrad ◽  
Marco Picasso ◽  
Gilles Steiner
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Sediment Transport ◽  
Splitting Method ◽  
Free Surface Flows ◽  
Surface Flows

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.

A Splitting Method for Numerical Simulation of Free Surface Flows of Incompressible Fluids with Surface Tension

2015 ◽  
Vol 15 (1) ◽  
pp. 59-77 ◽  
Author(s):  
Kirill D. Nikitin ◽  
Maxim A. Olshanskii ◽  
Kirill M. Terekhov ◽  
Yuri V. Vassilevski
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Stability Result ◽  
Free Surface Flows ◽  
Fluid Inertia ◽  
Time Step ◽  
Surface Flows ◽  
Level Set Function

AbstractThe paper studies a splitting method for the numerical time-integration of the system of partial differential equations describing the motion of viscous incompressible fluid with free boundary subject to surface tension forces. The method splits one time step into a semi-Lagrangian treatment of the surface advection and fluid inertia, an implicit update of viscous terms and the projection of velocity into the subspace of divergence-free functions. We derive several conservation properties of the method and a suitable energy estimate for numerical solutions. Under certain assumptions on the smoothness of the free surface and its evolution, this leads to a stability result for the numerical method. Efficient computations of free surface flows of incompressible viscous fluids need several other ingredients, such as dynamically adapted meshes, surface reconstruction and level set function re-initialization. These enabling techniques are discussed in the paper as well. The properties of the method are illustrated with a few numerical examples. These examples include analytical tests and the oscillating droplet benchmark problem.

Sign in / Sign up

Export Citation Format

Share Document