Deterministic sensitivity analysis of two-phase flow systems: Forward and adjoint methods

A self-contained mathematical formalism for deterministic sensitivity analysis of two phase flow systems, a detailed application to sensitivity analysis of the homogeneous equilibrium model of two phase flow, and a representative application to sensitivity analysis of a model where a transition between single phase and two phase occurs are presented. The rigor and generality of this sensitivity analysis formalism stem from the use of Gateaux (G-) differentials. The major aspects of deterministic sensitivity analysis which include derivation of the forward sensitivity equations, derivation of sensitivity expressions in terms of adjoint functions, explicit construction of the adjoint system satisfied by these adjoint functions, determination of the characteristics of this adjoint system, and demonstration that these characteristics are the same as those of the original quasilinear two phase flow equations are highlighted. It is proven that whenever the original two phase flow problem is solvable, the adjoint system is also solvable and the same numerical methods can be used to solve both the original and adjoint equations.