NONLINEAR PARAMETER ESTIMATION IN INVISCID COMPRESSIBLE FLOWS IN PRESENCE OF UNCERTAINTIES

摘要

The focus of this paper is on the formulation and solution of inverse problems of parameter estimation using algorithmic differentiation.The inverse problem formulated here seeks to determine the input parameters that minimize a least squares functional with respect to certain target data.The formulation allows for uncer- tainty in the target data by considering the least squares functional in a stochastic basis described by the covariance of the target data.Furthermore,to allow for robust design,the formulation also accounts for un- certainties in the input parameters.This is achieved using the method of propagation of uncertainties using the directional derivatives of the output parameters with respect to unknown parameters.The required derivatives are calculated simultaneously with the solution using generic programming exploiting the tem- plate and operator overloading features of the C++language.The methodology described here is general and applicable to any numerical solution procedure for any set of governing equations but for the purpose of this paper we consider a finite volume solution of the com- pressible Euler equations.In particular,we illustrate the method for the case of supersonic flow in a duct with a wedge.The parameter to be determined is the inlet Mach number and the target data is the axial component of velocity at the exit of the duct.