A multi-grid finite-volume method for free-surface flows (original) (raw)
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Multiple grid solution of the open channel flow equations using a marching finite-volume method
Advances in Water Resources, 1991
A multi-grid algorithm has been developed to accelerate the convergence solution of the open channel flow equations to obtain the steady flow. The scheme is constructed by combining the multiple-grid technique with a new marching finite-volume numerical solution. In the multi-grid application the corrections to the fine grid points are transferred to a coarse grid to maintain the low truncation errors associated with a fine level of discretizations. Distribution formulae are then used to propagate the changes onto selected coarser grid points. After applying interpolation to coarse grid corrections, the flow properties at every grid point of the fine mesh are updated. The channel flow will be assumed to be 2D, steady and viscous with wind and Coriolis forces neglected. The flow is also assumed to be fully mixed in the vertical direction. The general technique used is a combination of the finite-element and finite-difference methods. The governing PDE are transformed into an equivalent system applied over a square-grid network. Convergence histories are presented for supercritical flows as well as for super-critical flows with hydraulic jump presence. Numerical results indicate that substantial computational savings for the solution accuracy can be achieved.
Two-dimensional, Multi-grid, Viscous, Free-Surface Flow Calculation
1998
A two-dimensional subcritical and/or supercritical, viscous, free-surface flow calculation method is employed. A very important feature of the method is its simplicity and the physical understanding obtained from the solution procedure. The grid used may be irregular and conforms to the physical boundaries of the problem. A multi-grid algorithm has been developed to accelerate the convergence solution. The viscous flow stresses are described using either fixed value eddy viscosity coefficient or values related to the flow properties. Applications regarding subcritical viscous flow near spur-dike and flow in a supercritical channel are reported. Calculated results are in good agreement with measurements and/or other numerical solution results. Convergence histories are presented and the results indicate that substantial computational savings for the solution accuracy can be achieved.
An implicit scheme for steady two-dimensional free-surface flow calculation
An implicit numerical scheme has been developed and subsequently applied to calculate steady, two-dimensional depth averaged, free-surface flow problems. The implicit form of the scheme gives fast convergence. The scheme is second order accurate and unconditionally stable. The free-surface flow equations are transformed into a non-orthogonal, boundary-fitted coordinate system so as to simulate with accuracy irregular geometries. The model is used to analyze a wide variety of hydraulic engineering problems including subcritical flow in a converging-diverging flume, supercritical flow at a channel expansion with various Froude numbers, and mixed sub-and supercritical flow in a converging channel. The computed results are compared with measurements as well as with other numerical solutions and satisfactory agreement is achieved.
Numerical Simulation of Free Surface Flows
Journal of Computational Physics, 1999
A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar to the volume of fluid (VOF) method, the numerical schemes used to solve the problem are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stokes problem are to be solved. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small rectangular cells, using a forward characteristic method. The generalized Stokes problem is solved using a finite element method on a fixed, unstructured mesh. Numerical results are presented for several test cases: the filling of an S-shaped channel, the filling of a disk with core, the broken dam in a confined domain.
An efficient semi-implicit subgrid method for free-surface flows on hierarchical grids
International Journal for Numerical Methods in Fluids, 2015
We present a new modelling strategy for improving the efficiency of computationally intensive flow problems in environmental free-surface flows. The approach combines a recently developed semi-implicit subgrid method with a hierarchical grid solution strategy. The method allows the incorporation of high-resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The subgrid method improves the efficiency of the hierarchical grid method by providing better solutions on coarse grids. The method is applicable to both steady and unsteady flows, but we particularly focus on river flows with steady boundary conditions. There, the combined hierarchical grid-subgrid method reduces the computational effort to obtain a steady state with factors up to 43. For unsteady models, the method can be used for efficiently generating accurate initial conditions on high-resolution grids. Additionally, the method provides automatic insight in grid convergence. We demonstrate the efficiency and applicability of the method using a schematic test for the vortex shedding around a circular cylinder and a real-world river case study.
A Novel Algorithm of Advection Procedure in Volume of Fluid Method to Model Free Surface Flows
In this study, the developed procedure of advection in volume of fluid (VOF) method is presented for free surface modeling. The fluid is assumed to be incompressible and viscous and therefore, Navier-Stokes and continuity are considered as governing equations. Applying Youngs’ algorithm in staggered grids, it is assumed that fluid particles in the cell have the same velocity of the cell faces. Therefore, fluxes to neighboring cells are estimated based on cell face velocities. However, these particles can show different velocities between two adjacent cell faces. In developed model, the velocity in mass center of fluid cell is evaluated to calculate fluxes from cell faces. The performance of the model is evaluated using some alternative schemes such as translation, rotation, shear test, and dam break test. These tests showed that the developed procedure improves the results when using coarse grids. Therefore, the Modified Youngs-VOF (MYV) method is suggested as a new VOF algorithm wh...
IMPLICIT NUMERICAL SIMULATION OF TWO- AND THREE-DIMENSIONAL FREE-SURFACE FLOW PROBLEMS
The present study proposes a finite-volume implicit numerical scheme for the simulation of two-and three-dimensional free-surface flow problems. The implicit form of the scheme guarantees fast convergence allowing the use of large time steps. The introduction of a non-orthogonal boundary-fitted coordinate system (local coordinates) makes it possible for the model to handle various types of boundary conditions with accuracy. In the case of two-dimensional flow problems, the conservative form of the equations of fluid dynamics is used while the Navier-Stokes equations in combination with the innovative technique of pseudocompressibility are used to describe mathematically the three-dimensional free-surface flow problems. The resulting flow equations are transformed into the local coordinate system and then are solved numerically. The three dimensional scheme is used to analyze the free-surface flow over a double-arc spillway which was mounted in a laboratory flume. Bottom pressures and water levels were measured at various points along the centerline. Successful comparisons between measurements and computed results ensure the credibility of the proposed scheme.
Explicit and Implicit Finite -Volume Methods for Depth Averaged Free-Surface Flows
Applied and Computational Mechanics, 2020
In recent years, much progress has been made in solving free-surface flow variation problems in order to prevent flood environmental problems in natural rivers. Computational results and convergence acceleration of two different (explicit and implicit numerical techniques) finite-volume based numerical algorithms, for depth-averaged subcritical and/or supercritical, free-surface, steady flows in channels, are presented. The implicit computational model is a bi-diagonal, finite-volume numerical scheme, based on MacCormack’s predictor-corrector technique and uses the semi-linearization matrices for the governing Navier-Stokes equations which are expressed in terms of diagonalization. This implicit numerical scheme puts primary emphasis to solution convergence using non-orthogonal local coordinate system. The explicit formulation uses volume integrals to solve the governing flow equations. Computational results and convergence performance between the implicit and the explicit finite-vo...
Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids
Water, 2022
Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.
2017
The hydraulic flow channels are open conduits at atmospheric pressure which flow along a free surface. The hydraulic channel is a flow in free conduit, subject to the atmospheric pressure and can be realized in two ways: permanent and uniform and not permanent. The hydraulic conditions of flow and flow are determined through a systematic set of calculations and mathematical operations that will define the variable characteristics involved in the system. The motivation of the study of this relevant topic can be increased with the use of mathematical software used in engineering. The aim of the research was to study a rectangular hydraulic flow channel with the use of a computational tool. In this work the development of the program was through the App Designer of Matlab. A Pitot tube was used to determine the average flow velocity as a method of experimental validation. These data were obtained from the use of an experimental unit equipment in the ESAMC Santos hydraulics laboratory. This channel allows to vary the flow through a scalar potentiometer and to change the slope with the aid of a hydraulic jack. The flow velocity data were obtained by Santos et al.