Related papers: Analytic Full Potential Adjoint Solution for Two-d…
We obtain the analytic adjoint solution for two-dimensional (2D) incompressible potential flow for a cost function measuring aerodynamic force using the connection of the adjoint approach to Green's functions and also by establishing and…
The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution…
The complex potentials representing flows around a vertical plate semi-submerged in a uniform stream are derived in analytical forms by the reduction method. They are composed from the regular solution and a weak singular eigen solution.…
This paper considers the formulation of the adjoint problem in two dimensions when there are shocks in the flow solution. For typical cost functions, the adjoint variables are continuous at shocks, where they have to obey an internal…
The characteristic structure of the two-dimensional adjoint Euler equations is examined. The behavior is similar to that of the original Euler equations, but with the information travelling in the opposite direction. The compatibility…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…
The efficient method for computing the sensitivities is the adjoint method. The cost of solving an adjoint equation is comparable to the cost of solving the governing equation. Once the adjoint solution is obtained, the sensitivities to any…
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…
Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by the incorporation of the self-adjoint extension method to the path integral formalism. The energy-dependent Green functions for free particle plus…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…
Energy-dependent Green's functions for the two and three dimensional $\delta$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function…
One-dimensional $\delta^{'}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent…
A novel adjoint-based framework oriented to optimal flow control in compressible direct numerical simulations is presented. Also, a new formulation of the adjoint characteristic boundary conditions is introduced, which enhances the…
Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a…
Adjoints are used in optimization to speed-up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first order time derivatives, boundary conditions and transmission…
Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential…
This paper describes an exact solution to the drag-based adjoint Euler equations in two and three dimensions that is valid for irrotational flows.
Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and…