A Reduced-Order Extrapolation Spectral-Finite Difference Scheme Based on the POD Method for 2D Second-Order Hyperbolic Equations

In this study, a reduced-order extrapolation spectral-finite difference (ROESFD) scheme based on the proper orthogonal decomposition (POD) method is set up for the two-dimensional (2D) second-order hyperbolic equations. First, the classical spectral-finite difference (CSFD) method for the 2D second-order hyperbolic equations and its stability, convergence, and flaw are introduced. Then, a new ROESFD scheme that has very few degrees of freedom but holds sufficiently high accuracy is set up by the POD method and its implementation is offered. Finally, three numerical examples are offered to explain the validity of the theoretical conclusion. This implies that the ROESFD scheme is viable and efficient for searching the numerical solutions of the 2D second-order hyperbolic equations

Automatic Generation of Near-Body Structured Grids

Numerical grid generation has been a bottleneck in the computational fluid dynamics process for a long time when using the structured overset grids. Many current structured overset grid generation schemes like the hyperbolic grid generation method require significant user interaction to generate good computational grids robustly. Other grid generation schemes like the elliptic grid generation method take a significant amount of time for grid calculation, which is not desirable for computational fluid dynamics. Herein a new grid generation method is presented that combines the hyperbolic grid generation scheme with the elliptic grid generation scheme that uses Poisson’s equation. The new scheme builds upon the strengths of the different techniques by first applying hyperbolic grid generation, which is very fast but sometimes fails in strong concavities, and then using elliptic grid generation to locally fix the problems where hyperbolic grid generation results are not acceptable for computational fluid dynamics calculation. The new technique is demonstrated in various examples that are known to cause problems for either hyperbolic or elliptic grid generation when applied alone. The computational speed of the combined scheme grid generation is also exanimated by comparing the results with hyperbolic and elliptic grid generation. The combined grid generation scheme is further implemented in Engineering Sketch Pad to get useful near-body structure grids based on the geometry of the model. Attributes in Engineering Sketch Pad are used to define the places where the surface and volume grids should be generated, while the tessellations are used to locate and project grid generation results and therefore boost grid generation speed. Three cases are tested to illustrate the implementation of the combined grid generation scheme in Engineering Sketch Pad

Numerical methods for the simulation of complex multi-body flows with applications for the integrated Space Shuttle vehicle

The following papers are presented: (1) numerical methods for the simulation of complex multi-body flows with applications for the Integrated Space Shuttle vehicle; (2) a generalized scheme for 3-D hyperbolic grid generation; (3) collar grids for intersecting geometric components within the Chimera overlapped grid scheme; and (4) application of the Chimera overlapped grid scheme to simulation of Space Shuttle ascent flows

On computations of the integrated space shuttle flowfield using overset grids

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield

Fast prediction of transonic aeroelasticity using computational fluid dynamics

The exploitation of computational fluid dynamics for non linear aeroelastic simulations is mainly based on time domain simulations of the Euler and Navier-Stokes equations coupled with structural models. Current industrial practice relies heavily on linear methods which can lead to conservative design and flight envelope restrictions. The significant aeroelastic effects caused by nonlinear aerodynamics include the transonic flutter dip and limit cycle oscillations. An intensive research effort is underway to account for aerodynamic nonlinearity at a practical computational cost.To achieve this a large reduction in the numbers of degrees of freedoms is required and leads to the construction of reduced order models which provide compared with CFD simulations an accurate description of the dynamical system at much lower cost. In this thesis we consider limit cycle oscillations as local bifurcations of equilibria which are associated with degenerate behaviour of a system of linearised aeroelastic equations. This extra information can be used to formulate a method for the augmented solve of the onset point of instability - the flutter point. This method contains all the fidelity of the original aeroelastic equations at much lower cost as the stability calculation has been reduced from multiple unsteady computations to a single steady state one. Once the flutter point has been found, the centre manifold theory is used to reduce the full order system to two degrees of freedom. The thesis describes three methods for finding stability boundaries, the calculation of a reduced order models for damping and for limit cycle oscillations predictions. Results are shown for aerofoils, and the AGARD, Goland, and a supercritical transport wing. It is shown that the methods presented allow results comparable to the full order system predictions to be obtained with CPU time reductions of between one and three orders of magnitude