In this paper we present a unigrid multi–model formulation for transonic flow calculations based on solving, in sequence, the full potential equation and the the Euler equations. The goal is to minimize the overall computation time to simulate steady flows by using a more computational efficient physical model in the early iteration steps. The proposed method is based on two steps. In the first...

This paper is intended to reveal some new aspects of the principle of work and energy in its differential form. A theorem is given to state the principle of work and energy in differential form that can be applied alone to build up all the dynamical equations of a special class of MDOF mechanical systems. Some illustrations and discussions are presented to demonstrate the refined applicability ...

In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(OD...

Abstract: Shape variational formulation for Euler flow has already been considered by the author in (1999a, 2007c). We develop here the control approach considering the convection (or mass transport) as the “state equation” while the speed vector field is the control and we introduce the h-Sobolev curvature which turns to be shape differentiable. The value function defines a new shape metric; w...

The key equation describing the rotational dynamics of a rigid body is \({\vec \tau } = \text{d}{\vec L} / dt\) which can be understood based on Newton’s second and third laws motion together with assumption mutual centrality internal forces valid in an inertial coordinate system. While this written down by observer, for practical purposes, it efficiently worked out within non-inertial rotating...

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D. Ebin’s long-time existence result for geodesics on the symplectomorphism group to metrics not necessarily compatible with the symplectic structure. We also study the dynamics of symplectic point vortices, desc...

We present an α-regularization of the Birkhoff-Rott equation, induced by the two-dimensional Euler-α equations, for the vortex sheet dynamics. We show the convergence of the solutions of Euler-α equations to a weak solution of the Euler equations for initial vorticity being a finite Radon measure of fixed sign, which includes the vortex sheets case. We also show that, provided the initial densi...

This paper shows that standard empirical methods for estimating log-linearized consumption Euler equations cannot successfully uncover structural parameters like the coefficient of relative risk aversion from a dataset of simulated consumers behaving exactly according to the standard model. Furthermore, consumption growth for the simulated consumers is very highly statistically related to predi...

This paper presents an Euler and boundary-layer method capable of unsteady flow and aeroelastic simulations. An integral boundary-layer solver is coupled with an Euler solver in a “semi-inverse” manner. For the inviscid part, approximate wall boundaryconditions are implemented on non-moving mean chord positions, whereas the full nonlinear Euler equation is solved in the field for accurate resol...