scholarly journals Discrete adjoint methodology for general multiphysics problems

2022 ◽  
Vol 65 (1) ◽  
Author(s):  
Ole Burghardt ◽  
Pedro Gomes ◽  
Tobias Kattmann ◽  
Thomas D. Economon ◽  
Nicolas R. Gauger ◽  
...  
Keyword(s):  
Shape Sensitivity ◽  
Algorithmic Differentiation ◽  
Coupled Problem ◽  
Reverse Mode ◽  
Discrete Adjoint ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Design Software ◽  
Adjoint Solutions ◽  
Multiphysics Problems

AbstractThis article presents a methodology whereby adjoint solutions for partitioned multiphysics problems can be computed efficiently, in a way that is completely independent of the underlying physical sub-problems, the associated numerical solution methods, and the number and type of couplings between them. By applying the reverse mode of algorithmic differentiation to each discipline, and by using a specialized recording strategy, diagonal and cross terms can be evaluated individually, thereby allowing different solution methods for the generic coupled problem (for example block-Jacobi or block-Gauss-Seidel). Based on an implementation in the open-source multiphysics simulation and design software SU2, we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a heat exchanger (conjugate heat transfer), a deforming wing (fluid–structure interaction), and a cooled turbine blade where both effects are simultaneously taken into account.

An Investigation Into the Compliance of SCARA Robots. Part II: Experimental and Numerical Validation

1988 ◽  
Vol 110 (1) ◽  
pp. 23-30 ◽  
Author(s):  
H. A. ElMaraghy ◽  
B. Johns
Keyword(s):  
Elastic Compliance ◽  
Servo Control ◽  
Compliance Matrix ◽  
End Effector ◽  
Prismatic Parts ◽  
Numerical Solution Methods ◽  
Solution Methods ◽  
Using Data ◽  
Assembly Performance ◽  
Robot Configurations

A model of inherent elastic compliance was developed for general position-controlled SCARA, with conventional joint feedback control, for both rotational and prismatic part insertion (Part I). The developed model was applied to the SKILAM and ADEPT I robots for validation. Experimental procedures and numerical solution methods are described. It was found that the ADEPT I robot employs a coupled control strategy between joints one and two which produces a constant, decoupled end effector compliance. The applicable compliance matrix, in this case, is presented and the experimental results are discussed. The model may be used to develop compliance maps that define the amount of end effector compliance, as a function of the joints compliance, as well as its variation for different robot configurations. This is illustrated using data for the SKILAM SCARA robot. Results are plotted and discussed. The most appropriate robot postures for assembly were found for both rotational and prismatic parts. The conditions necessary to achieve compliance or semicompliance centers with the SKILAM robot were examined. The results and methods demonstrated in these examples may be used to select appropriate robots for given applications. They can also guide robot designers in selecting joint servo-control gains to obtain the desired joints compliance ratio and improve assembly performance.

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

2018 ◽  
Author(s):  
Anna Engels-Putzka ◽  
Jan Backhaus ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Unsteady Aerodynamics ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Algorithmic Differentiation ◽  
Design And Optimization ◽  
Initial Application ◽  
Reverse Mode ◽  
Geometric Changes

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values — e.g. performance data of a component — themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implemen-tational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

Nonequilibrium Continuum Traffic Flow Model with Frozen Sound Wave Speed

2003 ◽  
Vol 1852 (1) ◽  
pp. 183-192
Author(s):  
W. L. Jin ◽  
H. M. Zhang
Keyword(s):  
Traffic Flow ◽  
Sound Speed ◽  
Flow Model ◽  
Wave Model ◽  
Homogeneous System ◽  
Traffic Flow Model ◽  
Traffic Conditions ◽  
Numerical Solution Methods ◽  
Stable Conditions ◽  
Solution Methods

Results are presented from a recent study on a variation of a new non-equilibrium continuum traffic flow model in which traffic sound speed is constant. Hence this model is called the frozen-wave model. This model resembles the Payne–Whitham model but avoids the “back-traveling” of the latter. For this frozen-wave model, the Riemann problem is analyzed for its homogeneous system, two numerical solution methods are developed to solve it, and numerical simulations are carried out under both stable and unstable traffic conditions. These results show that under stable conditions, the model behaves similarly to the Payne–Whitham model. However, under unstable traffic conditions, it has nonphysical solutions or no solutions when a vacuum problem occurs. This study, on the one hand, provides a more complete picture of the properties of this frozen-wave model and reduces the risk of improper applications of it. On the other hand, it also highlights the need to adopt a density-dependent sound speed.

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