1. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 1. In the beginning CFD at Imperial College started with 2D parabolic flows. By Brian Spalding Title: Revival of the partially parabolic method: SIMPLE was created to permit extension to 3D parabolic flows. SIMPLE was quickly extended to 3D elliptic flows, which soon attracted most attention But computers being still small, the partially- parabolic method was then invented as a sometimes applicable compromise, saving memory at the expense of time.

2. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 2: before the digital age Airplanes appeared years before digital computers. Yet aerodynamicists could predict their lift and drag. They used a combination of potential-flow theory with boundary-layer theory: This proceeded by iteration. 1. First source-sink distributions were sought which caused streamlines to coincide with the shape of the airplane. 2. This led to distributions of pressure over the surface. 3.Then they used boundary-layer theory to calculate the ‘displacement thickness ‘of the layer, i.e. the extent to which the airplane was bigger than at first supposed. 4. So they repeated steps 1, 2, 3 to convergence.

3. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 3: Is the pre-computer method relevant today? Their boundary-layer theory was crude: two-dimensional :integral with assumed velocity profile. Therefore wind-tunnel tests were needed in addition. But the principle was sound. And it still is. For computers are still too small to allow adequately fine elliptic grids. Despite use of many sub-division levels.

4. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 4: A revived partially- parabolic method? The revived method would solve the potential elliptic Laplace equation outside boundary layer, wake and jet. Inside each of these it would solve 3D parabolic Navier-Stokes equations on as fine a grid as necessary (easy because only 2D storage is needed). Why should this not work? Why is it not used? Elliptic and parabolic solutions would alternate, exchanging domain-boundary information each time.

5. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 5: What about automobiles? Early PHOENICS needlessly solved elliptic Navier-Stokes far from the vehicle surface where the flow is inviscid. Near much of surface the flow is 3D parabolic And behind wheels and wing mirrors. But elliptic Navier-Stokes must be used for the wake;.

6. ASME Heat Transfer Conference Minneapolis July 2013 75 years of CFD/CHT Slide 7: What is needed for the implementation of this techniqe? All that is needed in order to implement such a multi- domain solution procedure is: There is plenty to do in the next 75 years. Other applications which can be envisaged include: Urban air-pollution (with a succession of downstream displaced 3d-elliptic domains) Wind farms (mainly parabolic with embedded elliptic sub-domains). a 3D Navier-Stokes code capable of both elliptic and parabolic operation (PHOENICS is); a generally applicable domain-to-domain data- interchange module (PHOENICS has this); a user-friendly problem-set-up and display module.