A completely conservative difference scheme of gas dynamics in orthogonal curvilinear coordinates

A completely conservative difference scheme in Eulerian curvilinear orthogonal coordinates is proposed for calculating discontinuous gas-dynamic flows on sufficiently coarse grids. The stability of the linear approximation of the proposed scheme is analyzed. Courant's condition provides a stability condition for this scheme.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 9–15, 1986.     

A conservative semi-Lagrangian method for multidimensional fluid dynamics applications

We describe a finite volume semi-Lagrangian method for the numerical approximation of conservation laws arising in fluid-dynamic applications. A discrete conservation relation is satisfied by using conservative interpolation for the material (or property) being conserved. The method was developed with a view to application in climate prediction. © 1995 John Wiley & Sons, Inc.     

A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates

In this paper, a robust and accurate high-resolution finite-volume scheme is presented which employs flux-vector splitting (FVS) as the building block for solution of shallow water equations in boundary-fitted curvilinear coordinates. Eddy viscosity approach is used to accommodate shear stresses due to turbulence. Splitting of the convective terms is achieved via flux Jacobians whereas Liou–Steffen Splitting (LSS) technique, but in transformed coordinates, is used to split pressure terms. Limited flux gradients are also used to increase the computational accuracy of evaluation of interface fluxes and decrease the excessive numerical dissipation associated with FVS. This will completely remove spurious oscillations in high-gradient regions without introducing too much numerical dissipations. The method is tested for some classic simulations including hydraulic jump, 1D dam break and 2D dam break problems. The results show very satisfactory agreement with experimental data, analytical solutions and other numerical results.     

求解无容量设施选址问题的半拉格朗日松弛新方法

无容量设施选址问题Un-capacitated Facility Location, UFL是应用于诸多领域的经典组合优化难题, 半拉格朗日松弛方法是求解UFL问题的一种精确方法. 分析了半拉格朗日松弛方法在求解UFL问题时所具有的性质, 在此基础上, 对求解UFL问题的半拉格朗日松弛方法进行了一定的理论完善, 并探讨了提高半拉格朗日松弛方法求解性能的有效途径.数值计算结果表明：改进方法具有明显的可行性和有效性.     

Viscous compressible stability investigations in cylindrical coordinates

A viscous stability code based on the linearized compressible Navier‐Stokes equations in cylindrical coordinates was developed. In this contribution, we discuss general aspects of its application and present some results on the stability of swirling jet flow at high subsonic Mach number. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

UPML formulation for truncating conductive media in curvilinear coordinates

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.     

The obstacle problem for shallow shells in curvilinear coordinates

Starting from the 3D Signorini problem in presence of a plane obstacle, we justify the limit inequation of unilateral contact posed in a 2D domain. In particular, we show that we can uncouple the three covariant components of the limit Kirchhoff–Love displacement field so that the non-penetrability condition involves only the “transverse” component as this is the case in Cartesian framework.     

A particle method to solve the Navier-Stokes system

Summary We extend to the case of the two-dimensional Navier-Stokes equations, a particle method introduced in a previous paper to solve linear convection-diffusion equations. The method is based on a viscous splitting of the operator. The particles move under the effect of the velocity field but are not affected by the diffusion which is taken into account by the weights. We prove the stability and the convergence of the method.     

A projection method to solve linear systems in tensor format

In this paper, we propose a method for the numerical solution of linear systems of equations in low rank tensor format. Such systems may arise from the discretisation of PDEs in high dimensions, but our method is not limited to this type of application. We present an iterative scheme, which is based on the projection of the residual to a low dimensional subspace. The subspace is spanned by vectors in low rank tensor format which—similarly to Krylov subspace methods—stem from the subsequent (approximate) application of the given matrix to the residual. All calculations are performed in hierarchical Tucker format, which allows for applications in high dimensions. The mode size dependency is treated by a multilevel method. We present numerical examples that include high‐dimensional convection–diffusion equations.Copyright © 2012 John Wiley & Sons, Ltd.     

From gas dynamics to pressureless gas dynamics

This paper is devoted to the convergence of solutions of the compressible Euler equations towards solutions of the pressureless gas dynamics system, when the pressure tends to 0. The goal is to prove accurate uniform bounds for particular solutions of the Euler equations.

     

A graphical method to solve a maximin allocation problem

This note extends a simple graphical method of a solving resource allocation problem, the objective function being the sum of returns developed by Vidal to the case where the objective function is of a maximin type.     

A multi-iterate method to solve systems of nonlinear equations

We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propose an explicit control of the numerical stability of the method.     

A linearization approach to solve the natural gas cash-out bilevel problem

In this article, we discuss a particular imbalance cash-out problem arising in the natural gas supply chain. This problem was created by the liberalization laws that regulate deals between a natural gas shipping company and a pipeline operator. The problem was first modeled as a bilevel nonlinear mixed-integer problem that considers the cash-out penalization for the final imbalance occurring in the system. We extend the original problem’s upper level objective function by including additional terms accounting for the gas shipping company’s daily actions aimed at taking advantage of the price variations. Then we linearize all the constraints at both levels in an equivalent way so as to make easier their numerical solution. The results of numerical experiments are compared with those obtained by the inexact penalization method proposed by the authors in previous papers.     

A Newton-type curvilinear search method for optimization

A new search method is presented for unconstrained optimization. The method requires the evaluation of first and second derivatives and defines a curve along which a undimensional step takes place. For large step-size, the method performs as Newton's method, but it does not fail where the latter fails. For small step-size, the method behaves as the gradient method.     

Conceptual linearization of Euler governing equations to solve high speed compressible flow using a pressure‐based method

The main objective of the current work is to introduce a new conceptual linearization strategy to improve the performance of a primitive shock‐capturing pressure‐based finite‐volume method. To avoid a spurious oscillatory solution in the chosen collocated grids, both the primitive and extended methods utilize two convecting and convected momentum expressions at each cell face. The expressions are obtained via a physical‐based discretization of two inclusive statements, which are constructed via a novel incorporation of the continuity and momentum governing equations. These two expressions in turn provide a strong coupling among the Euler conservative statements. Contrary to the primitive work, the linearization in the current work respects the definitions and essence of physics behind deriving the Euler governing equations. The accuracy and efficiency of the new formulation are then investigated by solving the shock tube as a problem with moving normal and expansion waves and the converging‐diverging nozzle as a problem with strong stationary normal shock. The results show that there is good improvement in performance of the primitive pressure‐based shock‐capturing method while its superior accuracy is not deteriorated at all. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

A graphical method to solve a family of allocation problems

This paper discusses the classical resource allocation problem. By very elementary arguments on Lagrangian duality it is shown that this problem can be reduced to a single one-dimensional maximization of a differentiable concave function. Moreover, a simple graphical method is developed and applied to a family of well-known problems from the literature.     

A feasible conjugate-direction method to solve linearly constrained minimization problems

An iterative procedure is presented which uses conjugate directions to minimize a nonlinear function subject to linear inequality constraints. The method (i) converges to a stationary point assuming only first-order differentiability, (ii) has ann-q step superlinear or quadratic rate of convergence with stronger assumptions (n is the number of variables,q is the number of constraints which are binding at the optimum), (iii) requires the computation of only the objective function and its first derivatives, and (iv) is experimentally competitive with well-known methods.For helpful suggestions, the author is much indebted to C. R. Glassey and K. Ritter.This research has been partially supported by the National Research Council of Canada under Grants Nos. A8189 and C1234.     

A new method to solve the damped nonlinear Klein-Gordon equation

This paper discusses a damped nonlinear Klein-Gordon equation in the reproducing kernel space and provides a new method for solving the damped nonlinear Klein-Gordon equation based on the reproducing kernel space.Two numerical examples are given for illustrating the feasibility and accuracy of the method.