Application of the reduced basis method to nonlinear transient thermal analysis

An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.