Research Projects

Renewed interest in planetary atmospheric entry, descent, and landing underscores the need for improved physics modeling in computational fluid dynamics. From a recent NASA solicitation, “the current state of the art for predicting aerothermal environments for planetary entry are dependent on physical models and underlying numerical methods that are, in many cases, two to five decades old.” Uncertainty in experimental data used in radiation heat transfer computations leads to, “over-engineering” of entry body heat shields, at a large weight and cost penalty. A method for computing gas emissivity and absorptivity from quantum mechanics principles is developed.

The approach is to cast the Schrõdinger wave equation as a discretized matrix eigenvalue problem which is solved using the ERAU parallel supercomputer. The numerical solutions for the wave functions are then integrated to determine the Einstein coefficients for emission and absorption, and hence the gas properties are tabulated as functions of temperature and pressure.

All of the published works we have found thus far assume Dirichlet or von Neumann boundary conditions for the eigenvalue problem. At best this presumes a priori knowledge of the solution. In general it is incorrect. The novel boundary condition treatment here admits simultaneous solution for several wave functions, unlike the “shooting methods” in most textbooks.

To date, numerical solutions for the hydrogen atom have been completed and compare very well with analytical solutions, and with experimental data maintained by National Institutes of Standards (NIST). The method is presently being extended to more complex species for which analytical solutions do not exist.