V.G. Ferreira

A Stable Semi-Implicit Method for Free Surface Flows

The present work is concerned with a semi-implicit modification of the GENSMAC method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in primitive varinbles formulation with a free surface. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The viscous terms are treated by the implicit backward method in time and a centered second order method in space, and the nonlinear convection terms are explicitly approximated by the high order upwind variable-order nonoscillatory scheme method in space. The boundary conditions at the free surface couple the otherwise segregated velocity and pressure fields. The present work proposes a method that allows the segregated solution of free surface flow problems to be computed by semi-implicit schemes that preserve the stability conditions of the related coupled semi-implicit scheme. The numerical method is applied to both the simulation of free surface and to confined flows. The numerical results demonstrate that the present technique eliminates the parabolic stabiliy restriction required by the original explicit GENSMAC method, and also found in segregated semi-implicit methods with time-lagged boundary conditions. For low Reynolds number flows, the method is robust and very efficient when compared to the original GENSMAC method.

Recent advances in the marker and cell method

SummaryIn this article recent advances in the MAC method will be reviewed. The MAC technique dates back to the early sixties at the Los Alamos Laboratories and this paper starts with a historical review, and then a summary of related techniques. Improvements since the early days of MAC (and the Simplified MAC-SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out all particles (markers) other than those near the free surface, more accurate approximations of the free surface boundary conditions, the addition of a bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamic) flow visualization facility. This article will concentrate, in the main, on a three-dimensional version of the SMAC method. It will show how to approximate curved boundaries by considering one configurational example in detail; the same will also be done for the free surface. The article will avoid validation, but rather focus on many of the examples and applications that the MAC method can solve from turbulent flows to rheology. It will conclude with some speculative comments on the future direction of the methodology.

Surface tension implementation for Gensmac 2D

In the present work we describe a method which allows the incorporation of surface tension into the GENSMAC2D code. This is achieved on two scales. First on the scale of a cell, the surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is estimated by fitting a least square circle to the free surface using the tracking particles in the cell and in its close neighbors. On a sub-cell scale, short wavelength perturbations are filtered out using a local 4-point stencil which is mass conservative. An efficient implementation is obtained through a dual representation of the cell data, using both a matrix representation, for ease at identifying neighbouring cells, and also a tree data structure, which permits the representation of specific groups of cells with additional information pertaining to that group. The resulting code is shown to be robust, and to produce accurate results when compared with exact solutions of selected fluid dynamic problems involving surface tension.

Simulation results and applications of an advection bounded scheme to practical flows

This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest. The numerical results are compared against analytical, numerical and experimental data and show good agreement with them. It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems.

Avaliação computacional de esquemas convectivos em problemas de dinâmica dos fluidos

This article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are analyzed and implemented in the context of normalized variables of Leonard. In order to access the performance of the schemes, Riemann problems for 1D Burgers, Euler and shallow water equations are considered. From the numerical results, the schemes are ranked according to their performance in solving these non-linear equations. The best scheme is then applied in the numerical simulation of tridimensional incompressible moving free surface flows.

NUMERICAL SOLUTIONS OF SHALLOW WATER EQUATIONSWITH SOURCE TERM USING HIGH-RESOLUTION BOUNDED UPWIND SCHEMES

This paper addresses the problem of obtaining numerical solutions of shallow water equations with source term when f ux limiters (ARORA-ROE, ADBQUICKEST, TOPUS, SUPERBEE andMINMOD)in upwindschemesare used. The numerical results show that these high-resolution upwindschemesprovidebetterresults thanthose obtain e

Expansão do Sistema FreeFlow-3D para Escoamentos com Influência da Temperatura

O objetivo do presente trabalho e estender o ambiente de simulacao FreeFlow-3D para a solucao numerica de problemas de escoamentos incompreessiveis, com superficies livres e com influencia de temperatura.

Análise e Implementação de Modelos de Turbulência K-E para Simulação de Escoamentos Imcompreessíveis Envolvendo Superfícies Livres e Rígidas

O bom desempenho do algoritmo numerico e o pre-requisito essencial para a simulacao de escoamentos em regime turbulento.