U. Jungnickel  G. Kielau  P. Maißer  A. Müller 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2009,89(1):44-53

The paper presents a generalization of the Helmholtz conditions for the existence of a first‐order kinetic potential (Lagrangian) in that cases where the motion equations of mechanical, electrical, or electromechanical systems are given in terms of nonholonomic velocities. It is assumed that the transformation between holonomic and nonholonomic velocities is known. It is shown how the generalized Helmholtz conditions for the simultaneous existence of a first‐order Lagrangian and a first‐order dissipation function follow from the generalized Helmholtz conditions for systems with holonomic velocities. Moreover, the classical Helmholtz conditions in case of nondissipative systems can be directly generalized to motion equations which include nonholonomic velocities. In both cases the Boltzmann‐Hamel equations are used. The approaches are demonstrated by two examples: a heavy gyroscope and a 3‐dimensional rotating electrical machine.  相似文献   

    

Masoud Darbandi  Shidvash Vakilipour 《国际流体数值方法杂志》2007,53(3):371-389

The numerical solution of the fluid flow governing equations requires the implementation of certain boundary conditions at suitable places to make the problem well‐posed. Most of numerical strategies exhibit weak performance and obtain inaccurate solutions if the solution domain boundaries are not placed at adequate locations. Unfortunately, many practical fluid flow problems pose difficulty at their boundaries because the required information for solving the PDE's is not available there. On the other hand, large solution domains with known boundary conditions normally need a higher number of mesh nodes, which can increase the computational cost. Such difficulties have motivated the CFD workers to confine the solution domain and solve it using artificial boundaries with unknown flow conditions prevailing there. In this work, we develop a general strategy, which enables the control‐volume‐based methods to close the outflow boundary at arbitrary locations where the flow conditions are not known prior to the solution. In this regard, we extend suitable conservative statements at the outflow boundary. The derived statements gradually detect the correct boundary conditions at arbitrary boundaries via an implicit procedure using a finite element volume method. The extended statements are validated by solving the truncated benchmark backward‐facing step problem. The investigation shows that the downstream boundary can pass through a recirculation zone without deteriorating the accuracy of the solution either in the domain or at its boundaries. The results indicate that the extended formulation is robust enough to be employed in solution domains with unknown boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

    

F. Zaouch 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2006,86(7):521-538

The time‐dependent Ginzburg‐Landau equations describe the state of a superconducting material. The case of time‐periodic applied magnetic field implies the existence of periodic orbits. Sufficient conditions are given here that, if satisfied, guarantee the stability of some associated periodic solutions.  相似文献   

    

Xiangying Chen  Ge‐Cheng Zha 《国际流体数值方法杂志》2006,50(7):767-793

The non‐reflective boundary conditions (NRBC) for Navier–Stokes equations originally suggested by Poinsot and Lele (J. Comput. Phys. 1992; 101 :104–129) in Cartesian coordinates are extended to generalized coordinates. The characteristic form Navier–Stokes equations in conservative variables are given. In this characteristic‐based method, the NRBC is implicitly coupled with the Navier–Stokes flow solver and are solved simultaneously with the flow solver. The calculations are conducted for a subsonic vortex propagating flow and the steady and unsteady transonic inlet‐diffuser flows. The results indicate that the present method is accurate and robust, and the NRBC are essential for unsteady flow calculations. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

    

P. Rajesh Kanna  Manab Kumar Das 《国际流体数值方法杂志》2006,50(8):973-985

An attempt is made to find out the suitable entrainment and exit boundary conditions in laminar flow situations. Streamfunction vorticity formulation of the Navier–Stokes equations are solved by ADI method. Two‐dimensional laminar plane wall jet flow is used to test different forms of the boundary conditions. Results are compared with the experimental and similarity solution and the proper boundary condition is suggested. The Kind 1 boundary condition is recommended. It consists of zero first derivative condition for velocity variable and for streamfunction equation, mixed derivative at the entrainment and exit boundaries. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

    

M. Ferrand  D. R. Laurence  B. D. Rogers  D. Violeau  C. Kassiotis 《国际流体数值方法杂志》2013,71(4):446-472

Wall boundary conditions in smoothed particle hydrodynamics (SPH) is a key issue to perform accurate simulations. We propose here a new approach based on a renormalising factor for writing all boundary terms. This factor depends on the local shape of a wall and on the position of a particle relative to the wall, which is described by segments (in two‐dimensions), instead of the cumbersome fictitious or ghost particles used in most existing SPH models. By solving a dynamic equation for the renormalising factor, we significantly improve traditional wall treatment in SPH, for pressure forces, wall friction and turbulent conditions. The new model is demonstrated for cases including hydrostatic conditions for still water in a tank of complex geometry and a dam break over triangular bed profile with sharp angle where significant improved behaviour is obtained in comparison with the conventional boundary techniques. The latter case is also compared with a finite volume and volume‐of‐fluid scheme. The performance of the model for a two‐dimensional laminar flow in a channel is demonstrated where the profiles of velocity are in agreement with the theoretical ones, demonstrating that the derived wall shear stress balances the pressure gradient. Finally, the performance of the model is demonstrated for flow in a schematic fish pass where both the velocity field and turbulent viscosity fields are satisfactorily reproduced compared with mesh‐based codes. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

    

E. Albin  Y. D'Angelo  L. Vervisch 《国际流体数值方法杂志》2012,68(5):546-563

A specific (hybrid) arrangement of variables is discussed to solve reactive compressible Navier–Stokes equations on staggered‐like grids with high‐order finite difference schemes. The objective is to improve the numerical flow solution at boundaries. Hybrid arrangement behaviour is compared with ‘pure’ colocated and staggered strategies. Classical Fourier analysis shows accuracy to be significantly improved in the hybrid case. One‐dimensional laminar flame test demonstrates increased robustness (in terms of mesh resolution), whereas computation of 1D exiting pressure wave propagation gives evidence that the method also improves accuracy in the prediction of non‐reflecting outflows, compared e.g. with the fully staggered scheme of (J. Comput. Phy. 2003). Multidimensional extension is illustrated through turbulent 2D planar and 3D expanding flames simulations. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Yuan Li  Rong An 《国际流体数值方法杂志》2012,69(3):550-566

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

R. Steijl  G. Barakos 《国际流体数值方法杂志》2012,69(8):1326-1349

This paper focuses on coupling methods for hybrid Navier–Stokes/molecular dynamics (MD) simulations. The computational domain is split in a continuum flow region, where a finite‐volume discretisation of the Navier–Stokes equations is used, and one or more particle domains, where molecular level modelling of the flow is employed. The domains are defined with a partial overlap, in which the flow states are coupled through an exchange of the velocity components. For the steady flows considered, an under‐relaxed Newton iteration method is used to drive the coupled system to convergence. The main focus of the present work is on methods to impose nonperiodic boundary conditions on the particle domain(s). A particle forcing is applied in the direction normal to the particle domain boundary to impose the boundary normal velocity component. A novel aspect of the present work is the extension of this method to more general nonplanar particle domain boundaries. The main contribution of the paper is the development of a particle forcing method in the direction tangential to the domain boundary, which is based on the equivalent continuum‐flow boundary shear stresses along with an iterative forcing strength adjustment based on the extrapolated particle boundary velocity. Furthermore, an adaptation scheme is presented, which uses the finite‐volume flux residuals of the particle bin averaged velocity field as a truncation criterion for the iterative force‐update scheme. It is demonstrated that by comparing the residual reduction for the momentum equation in the nonhomogeneous directions during the molecular dynamics simulations with that for a homogeneous direction, the forcing iteration at which the statistical noise in the velocity field dominates the uncertainty in the forcing strength can be determined. At this point the iteration can be truncated. It is shown that with adaptive schemes of this type, the total number of MD evaluations required in a coupled Navier–Stokes/MD simulation can be reduced relative to a hybrid scheme with a fixed number of forcing‐strength updates. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

W. Barthel  C. John  F. Trltzsch 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2010,90(12):966-982

In this work, boundary control problems governed by a system of semilinear parabolic PDEs with pointwise control constraints are considered. This class of problems is related to applications in the chemical catalysis. After discussing existence and uniqueness of the state equation with both linear and nonlinear boundary conditions, the existence of an optimal solution is shown. Necessary and sufficient optimality conditions are derived to deal with numerical examples, which conclude the paper.  相似文献