An efficient semi-implicit subgrid method for free-surface flows on hierarchical grids (original) (raw)

Semi-implicit subgrid modelling of three-dimensional free-surface flows

International Journal for Numerical Methods in Fluids, 2010

In this paper a semi-implicit numerical model for two-and three-dimensional free-surface flows will be formulated in such a fashion as to intrinsically account for subgrid bathymetric details. It will be shown that with the proposed subgrid approach the model accuracy can be substantially improved without increasing the corresponding computational effort.

A multi-grid finite-volume method for free-surface flows

AD Publication, 2018

Abstract—A depth-averaged subcritical and/or supercritical, steady, free-surface flow numerical model is developed to calculate physical hydraulic flow parameters in open channels. The vertically averaged free-surface flow equations are numerically solved using an explicit finite-volume numerical scheme in integral form. The grid used may be irregular and conforms to the physical boundaries of any problem. A multi-grid algorithm has been developed and has subsequently been applied to accelerate the convergence solution. A grid clustering technique is also applied. The numerical approach is straight forward and the flow boundary conditions are easy enforced. The capabilities of the proposed method are demonstrated by analyzing subcritical flow in an abrupt converging-diverging open channel flume as well calculating supercritical flows in an expansion channel. The computed results are satisfactorily compared with available measurements as well as with other numerical technique results. Very coarse grid gives satisfactory comparison results. The explicit numerical code can be utilized, within the assumptions made about the nature of the flow, for various vertically averaged free-surface flow calculations. Scope is to simulate free-surface flows of practical interest in a straight forward way. It can be extended to channel designs.

Calculation of flows using three-dimensional overlapping grids and multigrid methods

International Journal for Numerical Methods in Engineering, 1995

A computational methodology combining overlapping grid techniques with multigrid methods has been developed for three-dimensional flow calculations in or around complex geometries. The computational accuracy, efficiency and capability of the present approach are investigated in this paper. The incompressible Navier-Stokes equations are discretized using a finite volume method on a semi-staggered grid. The discrete problem is solved by a multigrid algorithm. Some numerical examples are chosen for evaluating numerical accuracy: (a) a straight pipe for which the exact solution is known; (b) curved pipes where previous experimental and numerical data are available; (c) an axisymmetric sudden expansion. The performance of the multigrid method on overlapping grids is assessed. Several cases of flows in stationary and timedependent complex geometries are given to demonstrate the capability and the potential of the methods that we employ.

Numerical Modelling and Analysis of Water Free Surface Flows∗

2005

Various environmental engineering applications related to water resources involve unsteady free surface flows. A full 3D models based on Navier-Stokes equations are a good description of the physical features concerning several phenomena as for example lake eutrophication, transport of pollutant, flood in rivers, watershed, etc. However these models are characterized by an important computational effort, that we aim to reduce in some case by the help of 2D models or by appropriate coupling models of different dimensions and by the use of the parallel algorithmic trough HPCN facilities. In this work, we present an overview of some approximations methodologies and techniques for an efficient numerical modelling of water free surface problems in a finite element context.

On implicit subgrid-scale modeling in wall-bounded flows

Physics of Fluids, 2007

Approaches to large eddy simulation where subgrid-scale model and numerical discretization are fully merged are called implicit large eddy simulation (ILES). Recently, we have proposed a systematic framework for development, analysis, and optimization of nonlinear discretization schemes for ILES [ Hickel et al., J. Comput. Phys. 213, 413(2006) ]. The resulting adaptive local deconvolution method (ALDM) provides a truncation error which acts as a subgrid-scale model consistent with asymptotic turbulence theory. In the present paper ALDM is applied to incompressible, turbulent channel flow to analyze the implicit model for wall-bounded turbulence. Computational results are presented for Reynolds numbers, based on friction velocity and channel half-width, of Reτ = 180, Reτ = 395, Reτ = 590, and Reτ = 950. All simulations compare well with direct numerical simulation data and yield better results than the dynamic Smagorinsky model at the same resolution. The results demonstrate that the implicit model ALDM provides an accurate prediction for wall-bounded turbulence although model parameters have been calibrated for the infinite Reynolds number limit of isotropic turbulence. The near-wall accuracy can be further improved by a simple modification which is described in the paper.

A computational multilevel approach for solving 2D Navier–Stokes equations over non-matching grids

Computer Methods in Applied Mechanics and Engineering, 2006

A multilevel approach with parallel implementation is developed for obtaining fast solutions of the Navier-Stokes equations solved on domains with non-matching grids. The method relies on computing solutions over different subdomains with different multigrid levels by using multiple processors. A local Vanka-type relaxation operator for the multigrid solution of the Navier-Stokes system allows solutions to be computed at the element level. The natural implementation on a multiprocessor architecture results in a straightforward and flexible algorithm. Numerical computations are presented, using benchmark applications, in order to support the method. Parallelization is discussed to achieve proper accuracy, load balancing and computational efficiency between different processors.

Residual based VMS subgrid modeling for vortex flows

Computer Methods in Applied Mechanics and Engineering, 2010

This paper presents a residual based subgrid modeling approach for Large Eddy Simulations (LES) based on the variational multiscale method as a cure for the problem of preservation of vortices in numerical flow simulation. This approach combines a splitting of the non-linear term in the Navier-Stokes equations into strain and vorticity with a residual based modeling of the subgrid problems. The benefit is that certain driving phenomena, normally not present in subgrid modeling, e.g. vortex stretching, can be seen in the equations.

Efficient Multigrid Techniques for the Solution of Fluid Dynamics Problems

Ph.D. Dissertation, 2013

The multigrid technique (MG) is one of the most efficient methods for solving a large class of problems very efficiently. One of these multigrid techniques is the algebraic multigrid (AMG) approach which is developed to solve matrix equations using the principles of usual multigrid methods. In this work, various algebraic multigrid methods are proposed to solve different problems including: general linear elliptic partial differential equations (PDEs), as anisotropic Poisson equation, problems with steep boundary layers, as convectional dominant convection-diffusion equations, and nonlinear system of equations as Navier-stokes equations. In addition, a new technique is introduced for solving convection-diffusion equation by predicting a modified diffusion coefficient (MDC) such that the discretization process applies on the modified equation rather than the original one. For a class of one-dimensional convection-diffusion equation, we derive the modified diffusion coefficient analytically as a function of the equation coefficients and mesh size, then, prove that the discrete solution of this method coincides with the exact solution of the original equation for every mesh size and/or equation coefficients. Extending the same technique to obtain analytic MDC for other classes of convection-diffusion equations is not always straight forward especially for higher dimensions. However, we have extended the derived analytic formula of MDC (of the studied class) to general convection-diffusion problems. The analytic formula is computed locally within each element according to the mesh size and the values of the associated coefficients in each direction. The numerical results for two-dimensional, variable coefficients, convection-dominated problems show that although the discrete solution does not coincide with the exact one, it provides stable and accurate solution even on coarse grids. As a result, multigrid-based solvers benefit from these accurate coarse grid solutions and retained its efficiency when applied for convection–diffusion equations. Many numerical results are presented to investigate the convergence of classical algebraic and geometric multigrid solvers as well as Krylov-subspace methods preconditioned by multigrid. Also, in this thesis, we were concerned with the channel flow, which is an interesting problem in fluid dynamics. This type of flow is found in many real-life applications such as irrigation systems, pharmacological and chemical operations, oil- v refinery industries, etc. In the present work, the channel flow with one and two obstacles are considered. The methodology is based on the numerical solution of the Navier-Stokes equations by using a suitable computational domain with appropriate grid and correct boundary conditions. Large-eddy simulation (LES) was used to handle the turbulent flow with Smagorinsky modeling. Finite- element method (FEM) was used for the discretization of the governing equations. Adaptive time stepping is used and the resulting linear algebraic systems are solved by different methods including preconditioned minimum residual method, geometric and algebraic multigrid methods. The investigation was carried out for a range of Reynolds number (Re) from 1 to 300 with a fixed blockage ratio β = 0.25 and an artificial source of turbulence is introduced in the inflow velocity profile to ensure the turbulent nature of the flow. The finite element method is used in the present work to discretize many CFD problems and we have developed algebraic multigrid (AMG) approaches for anisotropic elliptic equation, problems with steep boundary layers, as convectional dominant convection-diffusion equations, and nonlinear system of equations as Navier-stokes equations. The conclusions which are obtained in the present work can be stated as: (i) AMG can be used for many kinds of problems where the application of standard multigrid methods is difficult or impossible. (ii) Implementation of the proposed MDC technique produces the exact nodal solutions for the 1-D singularly-perturbed convection diffusion problems even on coarse grids with uniform or non-uniform mesh sizes. (iii) Numerical results show that extension of MDC to 2-D eliminates the oscillations and produces more accurate solutions compared with other existing methods. (iv) As a result, multigrid-based solvers retain its efficient convergence rates for singularly-perturbed convection diffusion problems. (v) Excellent convergence behavior is obtained for numerical solution of Navier-Stokes system for different values of Re in two cases, 1- and 2- obstacles, when we used the proposed AMG algorithm as a solver or a preconditioner of GMRES.

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.