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The numerical CTVD (Centered Total Variation Diminishing) scheme used in this study was successfully developed by Sanders and Li for compressible flows, especially for the high speed. Unified approach for incompressible flowsĪ unified approach for solving incompressible flows has been investigated in this study. Quantification of jet spreading, jet growth, nominal separation, and jet shrink effects due to corss flow are discussed. Simulation of laminar as well as turbulen wall jets is reported. The formulation employs boundary layer equations in an orthogonal curvilinear coordinate system. D.Ī computational model for the flow field of three dimensional incompressible wall jets prototypic of thrust augmenting ejectors with large cross flow is presented.
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The objective of the current talk, 'High-End Computing for Incompressible Flows', is to discuss some of the current issues in large scale computing for mission-oriented tasks.Ī computational model for three-dimensional incompressible wall jets with large cross flow The objective of the First MIT Conference on Computational Fluid and Solid Mechanics (June 12-14, 2001) is to bring together industry and academia (and government) to nurture the next generation in computational mechanics. High-End Computing for Incompressible Flows We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow. We furthermore show how compatible model constraints can be combined to construct new subgrid- scale models that have desirable properties built into them.
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However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid- scale models. We show that these subgrid- scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid- scale models. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid- scale models that are based on the local velocity gradient. We furthermore summarize the requirements that subgrid- scale models have to satisfy in order to preserve these important mathematical and physical properties. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. In particular, we aim to consolidate a systematic approach of constructing subgrid- scale models, based on the idea that it is desirable that subgrid- scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. We study the construction of subgrid- scale models for large-eddy simulation of incompressible turbulent flows. Physical consistency of subgrid- scale models for large-eddy simulation of incompressible turbulent flows The Taylor-Goertler-like vortices are observed for Re = 1,000. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods.
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The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. Large-scale computation of incompressible viscous flow by least-squares finite element method