Fine Grid Numerical Solutions of Triangular Cavity Flow

Numerical solutions of 2-D steady incompressible flow inside a triangular cavity are presented. For the purpose of comparing our results with several different triangular cavity studies with different triangle geometries, a general triangle mapped onto a computational domain is considered. The Navier-Stokes equations in general curvilinear coordinates in streamfunction and vorticity formulation are numerically solved. Using a very fine grid mesh, the triangular cavity flow is solved for high Reynolds numbers. The results are compared with the numerical solutions found in the literature and also with analytical solutions as well. Detailed results are presented

Comparison of Wide and Compact Fourth Order Formulations of the Navier-Stokes Equations

In this study the numerical performances of wide and compact fourth order formulation of the steady 2-D incompressible Navier-Stokes equations will be investigated and compared with each other. The benchmark driven cavity flow problem will be solved using both wide and compact fourth order formulations and the numerical performances of both formulations will be presented and also the advantages and disadvantages of both formulations will be discussed

Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers

Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601x601. The steady driven cavity solutions are computed for Re<21,000 with a maximum absolute residuals of the governing equations that were less than 10-10. A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature

Discussions on Driven Cavity Flow

The widely studied benchmark problem, 2-D driven cavity flow problem is discussed in details in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. Based on the several numerical and experimental studies, the fact of the matter is, above moderate Reynolds numbers physically the flow in a driven cavity is not two-dimensional. However there exist numerical solutions for 2-D driven cavity flow at high Reynolds numbers

Transient Solid Dynamics Simulations on the Sandia/Intel Teraflop Computer

Transient solid dynamics simulations are among the most widely used engineering calculations. Industrial applications include vehicle crashworthiness studies, metal forging, and powder compaction prior to sintering. These calculations are also critical to defense applications including safety studies and weapons simulations. The practical importance of these calculations and their computational intensiveness make them natural candidates for parallelization. This has proved to be difficult, and existing implementations fail to scale to more than a few dozen processors. In this paper we describe our parallelization of PRONTO, Sandia`s transient solid dynamics code, via a novel algorithmic approach that utilizes multiple decompositions for different key segments of the computations, including the material contact calculation. This latter calculation is notoriously difficult to perform well in parallel, because it involves dynamically changing geometry, global searches for elements in contact, and unstructured communications among the compute nodes. Our approach scales to at least 3600 compute nodes of the Sandia/Intel Teraflop computer (the largest set of nodes to which we have had access to date) on problems involving millions of finite elements. On this machine we can simulate models using more than ten- million elements in a few tenths of a second per timestep, and solve problems more than 3000 times faster than a single processor Cray Jedi

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies

Finite difference and cubic interpolated profile lattice boltzmann method for prediction of two-dimensional lid-driven shallow cavity flow

In this paper, two-dimensional lid-driven cavity flow phenomena at steady state were simulated using two different scales of numerical method: the finite difference solution to the Navier–Stokes equation and the cubic interpolated pseudo-particle lattice Boltzmann method. The aspect ratio of cavity was set at 1, 2/3, 1/2 and 1/3 and the Reynolds number of 100, 400 and 1,000 for every simulation condition. The results were presented in terms of the location of the center of main vortex, the streamline plots and the velocity profiles at vertical and horizontal midsections. In this study, it is found that at the simulation of Reynolds numbers 100 and 400, both methods demonstrate a good agreement with each other; however, small discrepancies appeared for the simulation at the Reynolds number of 1,000. We also found that the number, size and formation of vortices strongly depend on the Reynolds number. The effect of the aspect ratio on the fluid flow behavior is also presented