Related papers: Adjoint shape optimization from the continuum to f…
This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on…
When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…
This paper presents an implicit method for the discrete unified gas-kinetic scheme (DUGKS) to speed up the simulations of the steady flows in all flow regimes. The DUGKS is a multi-scale scheme finite volume method (FVM) for all flow…
Studying the feedback process of Active Galactic Nuclei (AGN) requires characterising multiple kinematical components, such as rotating gas and stellar disks, outflows, inflows, and jets. To compare the observed properties with theoretical…
Aerodynamic design optimization is an important problem in aircraft design that depends on the interplay between a numerical optimizer and a high-fidelity flow physics solver. Derivative-based, first and (quasi) second order, optimization…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
In this series of works, we develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating gas flows, where the molecular motion is confined to some prescribed directions but the speed is still a continuous…
In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the…
This paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a…
A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is…
In this paper we present a shape optimization scheme which utilizes the alternating direction method of multipliers (ADMM) to approximate a direction of steepest descent in $W^{1,\infty}$. The followed strategy is a combination of the…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
In complex, expensive optimization domains we often narrowly focus on finding high performing solutions, instead of expanding our understanding of the domain itself. But what if we could quickly understand the complex behaviors that can…
Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design…
A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…
This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite element method and a Discontinuous Galerkin (DG) method for the…
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or differential-algebraic equations. In this paper, we explore the geometric properties and develop methods…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure.…