A computer program written within the Mathematica software system automatically generates FORTRAN computer codes that numerically simulate, with high accuracy, the acoustical physics of complex unbounded three-dimensional or bounded two-dimensional flow fields. The program is a significant contribution to the field of computational aeroacoustics (CAA), which combines the traditional disciplines of acoustics and computational fluid dynamics (CFD). The program was developed, as a first step, to accelerate and facilitate analysis of noise generated by turbofan aircraft engines. It can also be applied in many other endeavors that involve the generation, propagation, and/or scattering of electromagnetic as well as acoustic waves, or in which there are requirements to obtain highly accurate solutions of systems of hyperbolic partial differential equations that describe physical phenomena in complex environments. Prior to the development of this program, considerable programming effort was necessary even to obtain a low-accuracy computer code for a typical application. The code generated automatically by this program is far more accurate and efficient.

Once the Problem Is Specified in terms of computational parameters (e.g., numbers of grid points) and geometric data, the FORTRAN code files needed to solve the problem are generated automatically.

In the original turbofan-noise application, there is a need for numerical-simulation software that has sufficient fidelity to simulate steep gradients in flow fields and that is efficient enough to run on today's computer systems. The present code-generator program was developed to satisfy this need and, more specifically, to create software that numerically solves the linearized Euler equations of flow on Cartesian grids in three-dimensional spatial domains that contain bodies with complex shapes.

The codes are based upon the recently developed Modified Expansion Solution Approximation (MESA) series of explicit finite-difference schemes. The essential idea behind the MESA schemes is to approximate the solutions of the partial differential equations instead of approximating the individual derivative terms. The MESA schemes use multidimensional spatial interpolation and the constructive procedure in the proof of the Cauchy-Kovalevsky theorem to develop a local series approximation to the solution of the system of partial differential equations in both space and time. MESA schemes provide spectrallike resolution with extraordinary efficiency and can, theoretically, offer levels of accuracy that are arbitrarily high in both space and time, without the inefficiencies of Runge-Kutta schemes. The MESA methods were originally developed in one and two dimensions with accuracy up to 11th order, but, in conjunction with the development of the present program, have been extended to three dimensions with accuracy up to 29th order in space and time.

Unfortunately, the complexity of the coding task in the original form of the MESA schemes was very high, so that in a given application, either the desired code could not be compiled or else it took an impractically long time to write the code in FORTRAN. The present code-generator program automatically codes the MESA schemes into FORTRAN. As part of the development of this program, the MESA schemes were reformulated into a very simple form, making it practical to use these schemes without the automation or, alternatively, making these schemes very powerful when the automation is used. The program provides means for treating grid-aligned solid wall boundaries in two dimensions with accuracy up to 11th order, and for treating generalized two-dimensional boundaries with accuracy up to second order. It also provides for automated parallelization of codes for execution on large-scale parallel computers.

This program is a "turnkey" code-generation software tool. Given input in the form of computational parameters plus a set of parametric curves that describe the object(s) that bound a flow field, the program automatically generates the code that simulates the acoustical physics of the flow field. The program thus relieves engineers and scientists of the traditionally labor-intensive tasks of generating computational grids, developing algorithms to solve the governing differential equations, coding the algorithms in FORTRAN, and ensuring that wall boundaries are treated correctly. By shifting these tasks to computers, the program can be expected to increase its users' productivity and capability. Additional work is required, however, to fully simulate bounded three-dimensional problems.

This work was done by Rodger W. Dyson and John W. Goodrich of Glenn Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Information Sciences category.

Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Glenn Research Center
Commercial Technology Office
Attn: Steve Fedor
Mail Stop 4—8
21000 Brookpark Road
Ohio 44135.

Refer to LEW-16970.

NASA Tech Briefs Magazine

This article first appeared in the June, 2000 issue of NASA Tech Briefs Magazine.

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