Numerical Scheme To Solve Unsteady And Variable Density Low Mach Number Flows PDF Download
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Author | : Mohamed Ahmed Fahmy Soliman |
Publisher | : |
Total Pages | : 288 |
Release | : 1988 |
Genre | : |
ISBN | : |
Download Numerical Scheme to Solve Unsteady and Variable Density Low Mach Number Flows Book in PDF, ePub and Kindle
Author | : B. Christer V. Johansson |
Publisher | : |
Total Pages | : 38 |
Release | : 1992 |
Genre | : Navier-Stokes equations |
ISBN | : |
Download The Numerical Solution of Low Mach Number Flow in Confined Regions by Richardson Extrapolation Book in PDF, ePub and Kindle
Abstract: "We use artificial compressibility together with Richardson extrapolation in the Mach number M as a method for solving the time dependent Navier-Stokes equation for very low Mach number flow and for incompressible flow. The question of what boundary conditions one should use for low Mach number flow, especially at inflow and outflow boundaries, is investigated theoretically, and boundary layer suppressing boundary conditions are derived. For the case of linearization around a constant flow we show that the low Mach number solution will converge with the rate O(M2) to the true incompressible solution, provided that we choose the boundary conditions correctly. However, if the boundary conditions are chosen incorrectly, it might happen that the low Mach number solution converges to an incompressible solution that looks physical, even though the difference between the true incompressible solution and the limit solution derived as M2 [->] 0 is O(1). The reason is that the limit solution in this case does not satisfy the boundary conditions. The results of numerical calculations for the time dependent, non-linear equations and for flow situations with time dependent inflow velocity profiles are presented. The convergence rate M2 to incompressible solution is numerically confirmed. It is also shown that using Richardson extrapolation to M2=0 in order to derive a solution with very small divergence can with good result be carried through with M2 as large as 0.1 and 0.05. As the time step in numerical methods must be chosen approximately such that [delta]t(i/M[delta]x + V/[delta]x2) is in the stability region of the time stepping method, and as M2=0.05 is sufficiently small to yield good results, the restriction on the time step due to the Mach number is not serious. Therefore the equations can be integrated very fast by explicit time stepping methods. This method for solving very low Mach number flow and incompressible flow is well suited to parallel processing."
Author | : |
Publisher | : |
Total Pages | : 988 |
Release | : 1989 |
Genre | : Aeronautics |
ISBN | : |
Download Scientific and Technical Aerospace Reports Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 12 |
Release | : 1993 |
Genre | : |
ISBN | : |
Download On Solving the Compressible Navier-Stokes Equations for Unsteady Flows at Very Low Mach Numbers Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 888 |
Release | : 1973 |
Genre | : Aeronautics |
ISBN | : |
Download STAR Book in PDF, ePub and Kindle
Author | : Thomas Schneider |
Publisher | : |
Total Pages | : 33 |
Release | : 1998 |
Genre | : Fluid dynamics |
ISBN | : |
Download Extension of Finite Volume Compressible Flow Solvers to Multi-dimensional, Variable Density Zero Mach Number Flow Book in PDF, ePub and Kindle
Abstract: "When attempting to compute unsteady, variable density flows at very small or zero Mach number using a standard finite volume compressible flow solver one faces at least the following difficulties: (i) Spatial pressure variations vanish as the Mach number M -> 0, but they do affect the velocity field at leading order; (ii) the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux; (iii) violation of this constraint would crucially affect the transport of mass, thereby disabling a code to properly advect even a constant density distribution. A previous companion paper derived the above observations from a single time - multiple length scale asymptotic analysis for M “1, applied to the conservation form of the governing equations and assuming an ideal gas with constant specific heats. The paper then restricted to weakly compressible one-dimensional flows and introduced a semi-implicit extension of a compressible flow solver, designed to handle the interaction of long wavelength acoustics with small scale, large amplitude density fluctuations. In the present paper we concentrate on the limit of zero Mach number for multi-demensional, variable density flows. The construction of numerical fluxes for all conserved quantities involves: An explicit upwind step (1) yielding predictions for the nonlinear convective flux components. This procedure still neglects the influence of pressure gradients on the convective fluxes during the time step. Suitable corrections are applied in step (2), which guarantees compliance of the convective fluxes with the divergence constraint. This step requires the solution of a Poisson-type equation to obtain the relevant pressure gradients. Step (3), which requires the solution of a second Poisson-type equation, yields the yet unknown (non-convective) pressure contribution to the total flux of momentum. The final cell centered velocity field exactly satisfies a discrete divergence constraint consistent with the asymptotic limit. Notice that step (1) can be done by any standard finite volume compressible flow solver and that the input to steps (2) and (3) involves solely the fluxes from step (1), but is independent on how these were obtained. Thus, we claim that our approach allows any such solver to be extended to simulate incompressible flows. Extensions to the weakly compressible regime 0
Author | : Eleuterio F. Toro |
Publisher | : Springer Science & Business Media |
Total Pages | : 635 |
Release | : 2013-04-17 |
Genre | : Technology & Engineering |
ISBN | : 366203915X |
Download Riemann Solvers and Numerical Methods for Fluid Dynamics Book in PDF, ePub and Kindle
High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.
Author | : Michael John Baines |
Publisher | : |
Total Pages | : 588 |
Release | : 1998 |
Genre | : Fluid dynamics |
ISBN | : |
Download Numerical Methods for Fluid Dynamics VI Book in PDF, ePub and Kindle
Author | : Marie Odile Bristeau |
Publisher | : Springer Science & Business Media |
Total Pages | : 350 |
Release | : 2013-03-08 |
Genre | : Technology & Engineering |
ISBN | : 3322878732 |
Download Numerical Simulation of Compressible Navier-Stokes Flows Book in PDF, ePub and Kindle
With the advent of super computers during the last ten years, the numerical simulation of viscous fluid flows modeled by the Navier-Stokes equations is becoming a most useful tool in Aircraft and Engine Design. In fact, compressible Navier-Stokes solvers tend to constitute the basic tools for many industrial applications occuring in the simulation of very complex turbulent and combustion phenomena. In Aerospace Engineering, as an exemple, their mathematical modelization requires reliable and robust methods for solving very stiff non linear partial differential equations. For the above reasons, it was clear that a workshop on this topic would be of interest for the CFD community in order to compare accuracy and efficiency of Navier-Stokes solvers on selected external and internal flow problems using different numerical approaches. The workshop was held on 4-6 December 1985 at Nice, France and organized by INRIA with the sponsorship of the GAMM Committee on Numerical Methods in Fluid Mechanics.
Author | : Yunho Jang |
Publisher | : |
Total Pages | : 150 |
Release | : 2004 |
Genre | : Mach number |
ISBN | : |
Download Direct Numerical Simulation of Variable Density Turbulence at Low Mach Number Book in PDF, ePub and Kindle