相关论文: Continuous Adjoint Complement to the Blasius Equat…

We propose a geometrically motivated mathematical model which reveals the key features of coastal and fluvial fragment shape evolution from the earliest stages of the abrasion. Our \textit{collisional polygon model} governs the evolution…

We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the…

Blasius boundary layer solution is a Maclaurin series expansion of the function \(f(\eta)\), which has convergence problems when evaluating for higher values of \(\eta\) due to a singularity present at \(\eta\approx-5.69\). In this paper we…

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…

In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…

Under this method second order \textbf{partial differential equations (PDE's)} can be reduce to first order PDE's, simplifying the Initial value problem \textbf{IVP} or Border value Problem \textbf{BVP} for most cases of second-order…

We consider flows of ordinary differential equations (ODEs) driven by path differentiable vector fields. Path differentiable functions constitute a proper subclass of Lipschitz functions which admit conservative gradients, a notion of…

A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative,…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

We establish that nonconvex definable parametric optimization problems with possibly nonsmooth objectives, inequality constraints, conic constraint systems, and non-unique primal and dual solutions admit an adjoint state formula under a…

This paper presents a "two-dimensional Fourier Continuation" method (2D-FC) for construction of bi-periodic extensions of smooth non-periodic functions defined over general two-dimensional smooth domains. The approach can be directly…

We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open…

We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in…

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.

It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. In this work, this oscillatory boundary layer theory is generalized to the case of linear viscoelastic(LVE) flow. We…

This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…

We give an unified framework to solve rough differential equations. Based on flows, our approach unifies the former ones developed by Davie, Friz-Victoir and Bailleul. The main idea is to build a flow from the iterated product of an almost…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…

An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…