相关论文: Analytic Adjoint Solutions for the 2D Incompressib…

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification…

We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics…

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…

A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization…

Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…

General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be…

This paper analyzes the adjoint solution of the Navier-Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, Re_D=20, 100 and 500. The quantity of interest in the adjoint formulation is the drag on the…

We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state…

Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…

We present a local existence result for the three dimensional incompressible Euler equations. The solution is constructed using a formulation of the equations as an active vector system in Eulerian coordinates. The formulation employs the…

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.…

The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…

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 present a new general method to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations of the theory relative to a diffeomorphic flow of curvilinear coordinates which…

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green…

The quasi-geostrophic equation or the Euler equation with dissipation studied in the present paper is a simplified form of the atmospheric circulation model introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205-1216] on the…

We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…