Adjoint Analysis for Heat Convection Design Optimization
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Solution Overview
Problem
Current design support systems for heat convection and mass diffusion fields require numerous numerical simulations to optimize design parameters, making them impractical for real-world applications due to time and resource constraints, especially when dealing with complex systems like data centers or electronic devices.
Innovation Solution
A design support system utilizing adjoint numerical analysis to reduce the number of simulations needed by performing forward analysis with initial boundary conditions and then using inverse analysis to determine sensitivity to design parameters, allowing for automatic optimization and visualization of design improvements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If forward problem approach with numerical simulation is used to obtain temperature distribution, then design parameters can be evaluated, but the number of simulations required increases rapidly with the number of designing parameters
Solution Approach 1:
The patent inverts the conventional forward problem approach by formulating and solving an adjoint problem. Instead of repeatedly running forward simulations to evaluate design parameters, the system solves a single adjoint problem to obtain sensitivity information for all design parameters simultaneously. This inversion transforms the computational burden from multiple forward simulations to one adjoint simulation, resolving the contradiction between evaluation accuracy and design efficiency.
Solution Approach 2:
The patent changes the mathematical formulation from evaluating parameters through forward simulations to computing sensitivities through an adjoint formulation. By transforming the problem into the adjoint domain, the system can evaluate the influence of multiple design parameters on thermal performance with a single computation, thereby improving productivity while maintaining measurement precision.
2Productivity
If inverse problem approach with adjoint formulation is used to evaluate parameter influence, then the number of simulations is reduced, but implementation complexity increases
Solution Approach 1:
The patent introduces an adjoint problem as an intermediary mathematical formulation that bridges the gap between forward simulations and sensitivity analysis. The adjoint formulation acts as a mediator that translates design parameter variations into thermal performance impacts without requiring multiple forward simulations. This intermediary approach reduces computational burden while managing implementation complexity through a systematic mathematical framework.
Solution Approach 2:
The patent replaces the mechanical iterative simulation process with a mathematical adjoint formulation. Instead of mechanically repeating forward simulations for each design parameter, the system substitutes this with a single adjoint problem solution that mathematically captures all parameter influences. This substitution reduces productivity loss while organizing complexity into a tractable mathematical structure.
3Manufacturing precision
If multiple numerical simulations are performed for optimization, then design accuracy improves, but computational time and resources increase significantly
Solution Approach 1:
The patent performs preliminary computation by solving the adjoint problem once to obtain sensitivity information for all design parameters. This preliminary action captures the essential relationships between design parameters and thermal performance, eliminating the need for repeated simulations during optimization. The adjoint solution serves as a pre-computed foundation that enables accurate design optimization without proportional increases in computational time.
Solution Approach 2:
The patent creates a mathematical copy of the forward problem in the adjoint domain. This adjoint copy contains the same physical relationships but is formulated to provide sensitivity information directly. By working with this mathematical copy rather than repeatedly executing the original forward problem, the system achieves the same design accuracy with significantly reduced computational time.
Data Source
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AI summary
Provides a general-purpose, highly convenient design support method and design support system for a heat convection field or a mass diffusion field which significantly reduce the number of times of numerical simulation required to examine the designing parameters for achieving the design purpose. The design support method comprises forward analysis step S3 of analyzing the heat convection field or the mass diffusion field by solving an equation of the heat convection field or the mass diffusion field based on an initially set value of a designing parameter; inverse analysis step S6 of analyzing a sensitivity defined by a change ratio of the design purpose to a designing parameter change by solving an adjoint equation corresponding to the design purpose based on the set design purpose; and sensitivity display step S7 of displaying information on the sensitivity analyzed by inverse analysis step S6 as a graphic image on the display device.