Solution Of Free Surface Flows Research Articles

Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows

A new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented. The algorithm is obtained by coupling a classical Finite Volume (FV) approach, that discretizes the Navier-Stokes equations on a block structured Eulerian grid, with an approach based on the Smoothed Particle Hydrodynamics (SPH) method, implemented in a Lagrangian framework. The coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time. A new algorithm for coupling meshless Lagrangian methods and Eulerian grid-based methods is proposed.A detailed validation using Smoothed Particle Hydrodynamics (SPH) and Finite Volume (FV) solvers is provided.To our knowledge this is the first time that a coupling like the present one is proposed, implemented and validated.The intrinsic characteristics of both solvers can be exploited to efficiently and accurately solve complex free-surface flows.The results prove that the coupling strategy is convenient from the point of view of both accuracy and computing time.

A dynamic interface compression method for VOF simulations of high-speed planing watercraft

A high speed surface craft is mostly supported by hydrodynamic lift force rather than by buoyancy force. The lift force directly influences the running attitude of the surface craft such as trim and sinkage. The pressure distribution is caused by a solution of free-surface flow around the surface craft. To deal with the free-surface flow, volume-of-fluid (VOF) method has been widely used even with its disadvantages including interface smearing. In the present study, a new dynamic interface compression method is introduced to reduce interface smearing and to avoid unphysical solutions. The method was validated by the volume fraction advection test and prismatic body problem. Finally, the method was applied to simulate the running attitude and resistance of several high speed planing vessels.

Unsteady mixed flows in non uniform closed water pipes: a Full Kinetic Approach

We recall the Pressurized and Free Surface model constructed for the modeling of unsteady mixed flows in closed water pipes where transition points between the free surface and pressurized flow are treated as a free boundary associated to a discontinuity of the gradient of pressure. Then we present a numerical kinetic scheme for the computations of unsteady mixed flows in closed water pipes. This kinetic method that we call FKA for “Full Kinetic Approach” is an easy and mathematically elegant way to deal with multiple transition points when the changes of state between free surface and pressurized flow occur. We use two approaches namely the “ghost waves approach” and the “Full Kinetic Approach” to treat these transition points. We show that this kinetic numerical scheme has the following properties: it is wet area conservative, under a CFL condition it preserves the wet area positive, it treats “naturally” the flooding zones and most of all it is very easy to implement it. Finally numerical experiments versus laboratory experiments are presented and the scheme produces results that are in a very good agreement. We also present a numerical comparison with analytic solutions for free surface flows in non uniform pipes: the numerical scheme has a very good behavior. A code to code comparison for pressurized flows is also conducted and leads to a very good agreement. We also perform a numerical experiment when flooding and drying flows may occur and finally make a numerical study of the order of the kinetic method.

Evaluation of Coupled Rheological Equations

Apart from the convergence of the first-order hyperbolic partial differential equations in rheological flow,this paper estimate the general behavior of the solution. By analyzing the coupled partial differential equations on a macroscopic scale the solution of free surface flow has been obtained. Its asymptotic estimate of the solution and super convergence are proposed in the internal boundary layer.

The challenge of mass conservation in the solution of free‐surface flows with the fractional‐step method: Problems and solutions

AbstractThe purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations for free‐surface flows has a problem inherent to the method that may produce unacceptable variations of the domain volume. A simple modification of the free‐surface boundary term is introduced in order to reduce considerably the volume loss and preserve the computational advantages of the FSM. Copyright © 2008 John Wiley & Sons, Ltd.

Operator splitting for the numerical solution of free surface flow at low capillary numbers

Free surface flows are pervasive in engineering and biomedical applications. In many interesting cases—particularly when small length scales are involved—surface forces (capillarity) dominate the flow dynamics. In these cases, computing the flow together with the shape of the surfaces, requires specialized solution techniques. This article investigates the capabilities of an operator splitting/finite elements method at handling accurately incompressible viscous flow with free surfaces at low capillary numbers. The test case of flow in the downstream section of a slot coater is used for three reasons: (1) it is an established benchmark; (2) it represents an idealized, yet industrially relevant flow; (3) high-fidelity results obtained with monolithic algorithms are available in literature. The flow and free surface shape attained with the new operator splitting scheme agree very satisfactorily with the results obtained with monolithic solvers. Because of its inherent computational simplicity, the new operator splitting scheme is attractive for large-scale simulations, three-dimensional flows, and flows of complex fluids.

An implicit boundary element solution with consistent linearization for free surface flows and non‐linear fluid–structure interaction of floating bodies

AbstractIn this work, a new comprehensive method has been developed which enables the solution of large, non‐linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian–Lagrangian approach has been translated into an implicit time‐integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid‐body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton–Raphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface flows.The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface flows and non‐linear fluid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid–structure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U‐shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization. Copyright © 2001 John Wiley & Sons. Ltd.

Parabolic numerical method for investigating free surface flows

Although one-dimensional analysis is a classical, accepted method used extensively in the literature and has been commonly used for the comparison with approximation methods for the solution of free surface flows, the requirement to specify the skin friction coefficient value has always been a constraint with which previous investigators have had trouble. The alternative method of solving the full Navier-Stokes equations requires substantial computer time because of the iteration necessary to resolve the location of the free surface boundary. A relatively simple parabolic numerical method for the thin-layer equations in two dimensions to solve the free surface flows without the need of assuming the skin friction coefficient and the need of iterating the free surface boundary is the purpose of this investigation. An order-of-magnitude analysis is used to reduce the elliptic governing Navier-Stokes equations to a parabolized set for high Reynolds numbers. The resulting equations are discretized and solved numerically for different sub and supercritical flows, various Pr, Fr, and Re numbers and for many different thermal boundary conditions using an implicit marching method employing the tridiagonal algorithm.

Spectral solution of free surface flows

A spectral Fourier-Chebyshev method for calculating unsteady two-dimensional free surface flows is presented and discussed. The vorticity-stream function equations are used in association with an influence matrix technique for prescribing the boundary and free surface conditions. The stability of the time-discretization scheme is analysed. Finally, numerical results are given for various physical problems.

A Study of Grid Dependence in Navier-Stokes Solutions for Free Surface Flows around a Ship Hull

Grid dependence in Navier-Stokes solution for free surface flows around a ship hull is investigated through numerical experiments. A Navier-Stokes solver used is a multigrid, finite-volume code with the artificial compressibility approach. Convection terms are evaluated by the third order upwind scheme based on the flux difference splitting. Time integration is carried out by the Runge-Kutta scheme. Nonlinear free surface conditions are implemented and a computational grid is re-generated to follow the free surface deformation. Free surface viscous flows around a Series 60 (Cb=0.6) hull are computed by the solver using three grids with different grid density. Solutions are compared with each other and with experimental data and grid dependence of solutions is discussed.