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Showing 1 to 14 of 14 for “"Sensitivity Equations"”.
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Aerodynamic Modeling Using Computational Fluid Dynamics and Sensitivity Equations
… frames. Generalized Navier-Stokes and Euler equations have been derived. The formulation is valid for all ranges of Mach numbers including transonic flow. The method was implemented numerically for the planar case using the generalized Euler equations. The developed computer codes can be used …
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Numerical Solution Techniques for Reaction Parameter Sensitivity Coefficients in Multicomponent Subsurface Transport Models
For reactive transport, the state equations consist of a nonlinear PDE for each aqueous component and a nonlinear ODE for each immobile component; these differential equations are coupled together through reaction source/sink terms. The corresponding sensitivity equations take the form of a system …
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Continuum Analytical Shape Sensitivity Analysis of 1-D Elastic Bar
In this thesis, a continuum sensitivity analysis method is presented for calculation of shape sensitivities of an elastic bar. The governing differential equations and boundary conditions for the elastic bar are differentiated with respect to the shape design parameter to derive the continuum …
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Parallel multigrid for large-scale least squares sensitivity
… is a novel approach to solving the "climate" sensitivity problem for periodic systems. A small change to the traditional adjoint sensitivity equations results in a method which can accurately compute both instantaneous and long-time averaged sensitivities. The second approach deals with the …
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Integrated Multidisciplinary Design Optimization Using Discrete Sensitivity Analysis for Geometrically Complex Aeroelastic Configurations
… unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed. The advantage of unstructured grids, when compared with a structured-grid approach, is their inherent ability to discretize irregularly shaped domains with greater efficiency and less …
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Computational Investigations of Boundary Condition Effects on Simulations of Thermoacoustic Instabilities
… presents a formulation of the Continuous Sensitivity Equation Method (CSEM) applied to the Computational Fluid Dynamics (CFD) simulation of thermoacoustic instability problems. The proposed sensitivity analysis approach only requires a single run of the CFD simulation. Moreover, the …
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Sensitivity analysis of oscillating hybrid systems
… on the dynamic behavior of such systems is sensitivity analysis. A theory for sensitivity analysis with respect to the initial conditions and/or parameters of oscillating hybrid systems is developed and discussed. Boundary-value formulations are presented for initial conditions, period, …
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Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems
… solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on …
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A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation
… of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem …
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Sensitivities in Option Pricing Models
… its importance. We derive the continuous adjoint equations with appropriate boundary conditions for three main option pricing models: the Black-Scholes model, the Heston's model and the jump diffusion model, for European type options. These adjoint equations can be used to compute the gradient of …
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Continuum Sensitivity Analysis using Boundary Velocity Formulation for Shape Derivatives
The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the …
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Continuum Sensitivity Method for Nonlinear Dynamic Aeroelasticity
In this dissertation, a continuum sensitivity method is developed for efficient and accurate computation of design derivatives for nonlinear aeroelastic structures subject to transient<br />aerodynamic loads. The continuum sensitivity equations (CSE) are a set of linear partial<br />differential …
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Reliability-Based Design Optimization of Nonlinear Beam-Columns
… beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on …
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Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems
Sensitivity analysis is a useful mathematical tool for many designers, engineers and mathematicians. This work presents a study of sensitivity equation methods for elliptic boundary value problems posed on parameter dependent domains. The current focus of our efforts is the construction of a …