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First-Order Comprehensive Adjoint Method For Computing Operator-Valued Response Sensitivities To Imprecisely Known Parameters, Internal Interfaces And Boundaries Of Coupled Nonlinear Systems: Ii. Application To A Nuclear Reactor Heat Removal Benchmark, Dan Gabriel Cacuci
Faculty Publications
This work illustrates the application of a comprehensive first-order adjoint sensitivity analysis methodology (1st-CASAM) to a heat conduction and convection analytical benchmark problem which simulates heat removal from a nuclear reactor fuel rod. This analytical benchmark problem can be used to verify the accuracy of numerical solutions provided by software modeling heat transport and fluid flow systems. This illustrative heat transport benchmark shows that collocation methods require one adjoint computation for every collocation point while spectral expansion methods require one adjoint computation for each cardinal function appearing in the respective expansion when recursion relations cannot be developed between the corresponding …
First-Order Comprehensive Adjoint Method For Computing Operator-Valued Response Sensitivities To Imprecisely Known Parameters, Internal Interfaces And Boundaries Of Coupled Nonlinear Systems: I. Mathematical Framework, Dan Gabriel Cacuci
Faculty Publications
This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently the first-order sensitivities (i.e., functional derivatives) of operator-valued responses (i.e., model results) of general models of coupled nonlinear physical systems characterized by imprecisely known or and/or uncertain parameters, external boundaries, and internal interfaces between the coupled systems. The explicit mathematical formalism developed within the 1st-CASAM for computing the first-order sensitivities of operator-valued response to uncertain internal interfaces and external boundaries in the models’ phase–space enables this methodology to generalize all of the previously published methodologies for computing first-order response sensitivities. The computational resources needed for using …