Computational fluid dynamics
Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows.
Probably the first work using computers to model fluid flow, as governed by the Navier–Stokes equations, was performed at Los Alamos National Lab, in the T3 group.
The first lifting Panel Code (A230) was described in a paper written by Paul Rubbert and Gary Saaris of Boeing Aircraft in 1968.
[12] In time, more advanced three-dimensional Panel Codes were developed at Boeing (PANAIR, A502),[13] Lockheed (Quadpan),[14] Douglas (HESS),[15] McDonnell Aircraft (MACAERO),[16] NASA (PMARC)[17] and Analytical Methods (WBAERO,[18] USAERO[19] and VSAERO[20][21]).
Its sister code, USAERO is an unsteady panel method that has also been used for modeling such things as high speed trains and racing yachts.
Developers turned to Full Potential codes, as panel methods could not calculate the non-linear flow present at transonic speeds.
[26] Frances Bauer, Paul Garabedian and David Korn of the Courant Institute at New York University (NYU) wrote a series of two-dimensional Full Potential airfoil codes that were widely used, the most important being named Program H.[27] A further growth of Program H was developed by Bob Melnik and his group at Grumman Aerospace as Grumfoil.
[28] Antony Jameson, originally at Grumman Aircraft and the Courant Institute of NYU, worked with David Caughey to develop the important three-dimensional Full Potential code FLO22[29] in 1975.
A derivative of MSES, for the design and analysis of airfoils in a cascade, is MISES,[40] developed by Harold Youngren while he was a graduate student at MIT.
A number of three-dimensional codes were developed (ARC3D, OVERFLOW, CFL3D are three successful NASA contributions), leading to numerous commercial packages.
Recently CFD methods have gained traction for modeling the flow behavior of granular materials within various chemical processes in engineering.
This approach has emerged as a cost-effective alternative, offering a nuanced understanding of complex flow phenomena while minimizing expenses associated with traditional experimental methods.
In the application of CFD, a critical step is to decide which set of physical assumptions and related equations need to be used for the problem at hand.
In a standard, low order FEM in 2D, for quadrilateral elements the most typical choice is the bilinear test or interpolating function of the form
Thus, high order Gauss integration quadratures are employed, since they achieve the highest accuracy with the smallest number of computations to be carried out.
At the time there are some academic CFD codes based on the spectral element method and some more are currently under development, since the new time-stepping schemes arise in the scientific world.
Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.
In this method, one works with the discrete in space and time version of the kinetic evolution equation in the Boltzmann Bhatnagar-Gross-Krook (BGK) form.
Software based on the vortex method offer a new means for solving tough fluid dynamics problems with minimal user intervention.
Regions near solid boundaries and where the turbulent length scale is less than the maximum grid dimension are assigned the RANS mode of solution.
DES is a non-zonal approach and provides a single smooth velocity field across the RANS and the LES regions of the solutions.
Goldstein and Vasilyev[66] applied the FDV model to large eddy simulation, but did not assume that the wavelet filter eliminated all coherent motions from the subfilter scales.
This approach is analogous to the kinetic theory of gases, in which the macroscopic properties of a gas are described by a large number of particles.
VC is similar to shock capturing methods, where conservation laws are satisfied, so that the essential integral quantities are accurately computed.
It is primarily used in one-dimensional representations of turbulent flow, since it can be applied across a wide range of length scales and Reynolds numbers.
By operating on multiple scales, multigrid reduces all components of the residual by similar factors, leading to a mesh-independent number of iterations.
[citation needed] For indefinite systems, preconditioners such as incomplete LU factorization, additive Schwarz, and multigrid perform poorly or fail entirely, so the problem structure must be used for effective preconditioning.
[74] Methods commonly used in CFD are the SIMPLE and Uzawa algorithms which exhibit mesh-dependent convergence rates, but recent advances based on block LU factorization combined with multigrid for the resulting definite systems have led to preconditioners that deliver mesh-independent convergence rates.
[75] CFD made a major break through in late 70s with the introduction of LTRAN2, a 2-D code to model oscillating airfoils based on transonic small perturbation theory by Ballhaus and associates.
To analyze these conditions, CAD models of the human vascular system are extracted employing modern imaging techniques such as MRI or Computed Tomography.
