Computational fluid dynamics

The Computational Fluid Dynamics (English: computational fluid dynamics, CFD) is an established method of fluid mechanics. It has the goal of fluid mechanical problems to solve approximate numerical methods. The model equations are usually used Navier -Stokes equations, the Euler 's equations or equations potential. The motivation for this is that important issues such as the calculation of the drag coefficient very quickly lead to non-linear problems that are solved exactly only in special cases. The computational fluid dynamics then provides an inexpensive alternative to tests in the wind tunnel or water channel.

The internationally accepted abbreviation CFD is used since about a conference of the AIAA 1973. Therein, the use of CFD has been established as a tool for the design of aircraft.

Models

The most comprehensive model, the Navier -Stokes equations. It is a system of nonlinear partial differential equations of 2nd order, which describe completely the most fluids. In particular, turbulence and the hydrodynamic boundary layer are included, however, which leads to the highest demands in computing power, memory, and the numerical methods.

A simpler model are the Euler 's equations which do not reflect a result of the friction neglected the boundary layer and do not contain any turbulence, which, for example, flow separation can not be simulated by the model. But are much coarser grid suitable for the equations to solve meaningful. For those parts of the flow where the boundary layer does not play a significant role, the Euler equations are very well suited.

The potential equations finally are useful especially when fast rough predictions to be made. For them, the entropy is assumed to be constant, which means that no strong shock waves can occur because of this, the entropy is even discontinuous. Further simplification on constant density then leads to the Laplace equation.

In multiphase flow interaction forces play a role between the phases, with appropriate simplifications can be performed.

CFD methods are also the basis for the numerical aeroacoustics, which deals with the calculation of flow noise.

Method

The most common solution methods for computational fluid dynamics are

• The finite difference method ( FDM)
• The finite volume method ( FVM)
• And the finite element method ( FEM).

The FEM is suitable for many problems, in particular for elliptic and parabolic in the incompressible range, less hyperbolic. It is characterized by robustness and solid mathematical underpinnings. FVM is suitable for conservation laws, especially for compressible flows. FDM is very simple and therefore mainly of theoretical interest.

More are

• The spectral method
• The Lattice Boltzmann Method ( LBM )
• The Smoothed Particle Hydrodynamics ( SPH)
• The boundary element method ( boundary element method BEM)

In all methods are numerical approximation methods that need to be compared for validation with quantitative experiments. With the exception of the particle- based methods, the starting point of the above methods is the discretization of the problem with a computational grid.

Time-dependent equations

For time- dependent equations, the order of spatial and time discretization leads to two different approaches:

• Vertical line method: Here is first discretized in place, so that one obtains a system of ordinary differential equations in time.
• Horizontal line method (or Rothe method): The time discretization is performed first, and the equations reduce to the solution of a boundary value problem at each time step.

The first method is used primarily for hyperbolic equations and compressible flows, the latter for incompressible flows. In addition, the method is flexible Rothe with respect to an implementation of an adaptive mesh refinement in place during the time evolution of the flow equations.

Turbulent flows

In turbulent flows, there are still many unanswered questions for the numerical flow simulation: either one uses very fine computational grid as in the direct numerical simulation or you can use more or less empirical turbulence models, in which not only numerical errors, additional modeling errors. Simple problems can be solved on high-end PCs in minutes, while complex 3D problems are even partially hardly be solved on mainframe computers.

Software

On the commercial side of the market of the products of ANSYS ( FLUENT, CFX ) and CD- adapco (Star -CCM ) is dominated, both based on the method of finite volume ( FVM). In the open source OpenFOAM area is the most widely used software package, which is also based on the FVM.

Especially for the Lattice Boltzmann method, there are other commercial and freely available solver.

In addition, there are a wide variety of solvers which are geared to specific flow problems and there are also used. At many universities solvers are developed which are enjoying great popularity especially in academic circles.

Details about the algorithms used are available in the above " method " linked articles. Extensive overviews of available applications and program code can be accessed via the following links:

• CFD -Online: An extensive list of CFD applications
• Astro- sim.org Open community for users and developers of astrophysical simulation codes. With list of freely available simulation codes and their properties.
• Different free CFD software