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

Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Skewed Cavity

The benchmark test case for non-orthogonal grid mesh, the "driven skewed cavity flow", first introduced by Demirdzic et al. (1992, IJNMF, 15, 329) for skew angles of alpha=30 and alpha=45, is reintroduced with a more variety of skew angles. The benchmark problem has non-orthogonal, skewed grid mesh with skew angle (alpha). The governing 2-D steady incompressible Navier-Stokes equations in general curvilinear coordinates are solved for the solution of driven skewed cavity flow with non-orthogonal grid mesh using a numerical method which is efficient and stable even at extreme skew angles. Highly accurate numerical solutions of the driven skewed cavity flow, solved using a fine grid (512x512) mesh, are presented for Reynolds number of 100 and 1000 for skew angles ranging between 15<alpha<165

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed

Finite elements with h -adaptation for momentum, heat and mass transport with application to environmental flow

Self-adaptive algorithms for 2 and 3-dimensional unstructured finite element grids are recent to the solution of partial differential equations, particularly those equations describing environmental transport. An h-adaptive grid embedding method is developed to solve the incompressible Navier-Stokes equations for fluid flow and scalar transport. An application to atmospheric mass transport is presented; This h-adaptive algorithm, in combination with the finite element method, has been designed to solve 2 and 3-dimensional problems on Pentium PC\u27s, including problems involving complex geometry on high end PC\u27s, workstations and mainframes. The Galerkin finite element solver is a 2 point Gauss-Legendre integration scheme which employs mass lumping, Cholesky skyline L-U decomposition, and Petrov-Galerkin upwinding; This dissertation introduces and explains the application of the Galerkin weighted residual finite element method. Development of the weak statements for the non-dimensional primitive variable Navier-Stokes equations is presented along with a Poisson formulation for resolving pressure. The semi-implicit solution process of this Poisson formulation is described in detail. Various adaptive methods are presented with emphasis on grid embedDing Finally the application of the adaptive process coupled with the finite element solver is applied to the solution of the Navier-Stokes equations along with the species transport equation; Adaptive methods are becoming common place in the solution of partial differential equations. In this thesis, an algorithm employing h-adaptation is developed for the solution of the non-linear Navier-Stokes equations for incompressible flow and its application to environmental fluid dynamics. Improvements in computational requirements are discussed including comparison with solutions on globally refined domains. Comparison of solutions is provided by using benchmark problems that provide a means for assuring the verification and validation of the computer code. Implementation of the algorithm for environmental species transport is an effective method to improve the accuracy of transport prediction