Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed. The ideas of low-Mach-number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density-based, time-marching schemes for solving flows of incompressible and variable density fluids at all speeds. The preconditioning is coupled with a dual time-stepping scheme implemented within an explicit, multistage algorithm for solving time-accurate flows. The resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured, solution-adaptive mesh topologies. This method is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids. The time-accurate solution of unsteady, incompressible flow is also demonstrated.

Preconditioning Applied to Variable and Constant Density Flows

A sequel to AUSM, Part II: AUSM+-up for all speeds

https://hal.inria.fr/inria-00073529/document

On the behaviour of upwind schemes in the low Mach number limit

▪ Abstract An overview of preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the preconditioning matrix.

Preconditioning techniques in computational fluid dynamics

We describe an algorithm for the solution of the Navier-Stokes equations on unstructured meshes that employs a coupled algebraic multigrid method to accelerate a point-implicit symmetric Gauss-Seidel relaxation scheme. The equations are preconditioned to permit solution of both compressible and incompressible flows. A cell-based, finite volume discretization is used in conjunction with flux-difference splitting and a linear reconstruction of variables. We present results for flowfields representing a range of Mach numbers and Reynolds numbers. The scheme remains stable up to infinite Courant number and exhibits CPU usage that scales linearly with cell count

Implicit Solution of Preconditioned Navier- Stokes Equations Using Algebraic Multigrid

Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes

A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.

Propulsion-related flowfields using the preconditioned Navier-Stokes equations

In this paper we describe an algorithm for the solution of the Navier-Stokes equations on unstructured meshes. The algorithm employs a coupled algebraic multigrid (AMG) method to accelerate a two-sweep point implicit Gauss-Siedel relaxation scheme. The equations are preconditioned to permit solution of both compressible and incompressible flows. A cellbased, finite-volume discretization is used in conjunction with flux difference splitting and a linear reconstruction of variables. We present results for flow fields representing a range of Mach numbers and Reynolds numbers. The scheme remains stable for infinite CFL number and exhibits CPU usage that scales linearly with cell count.

Jonathan M. Weiss

Papers

Preconditioning Applied to Variable and Constant Density Flows

Implicit Solution of Preconditioned Navier- Stokes Equations Using Algebraic Multigrid

Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes

Propulsion-related flowfields using the preconditioned Navier-Stokes equations

Implicit solution of the navier-stokes equations on unstructured meshes