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Boundary Treatment (boundary + treatment)
Selected AbstractsOn the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010I. Kalashnikova Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source] Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Dan Givoli Abstract A new finite element (FE) scheme is proposed for the solution of time-dependent semi-infinite wave-guide problems, in dispersive or non-dispersive media. The semi-infinite domain is truncated via an artificial boundary ,, and a high-order non-reflecting boundary condition (NRBC), based on the Higdon non-reflecting operators, is developed and applied on ,. The new NRBC does not involve any high derivatives beyond second order, but its order of accuracy is as high as one desires. It involves some parameters which are chosen automatically as a pre-process. A C0 semi-discrete FE formulation incorporating this NRBC is constructed for the problem in the finite domain bounded by ,. Augmented and split versions of this FE formulation are proposed. The semi-discrete system of equations is solved by the Newmark time-integration scheme. Numerical examples concerning dispersive waves in a semi-infinite wave guide are used to demonstrate the performance of the new method. Copyright © 2003 John Wiley & Sons, Ltd. [source] One-dimensional simulation of supercritical flow at a confluence by means of a nonlinear junction model applied with the RKDG2 methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008G. Kesserwani Abstract We investigate the one-dimensional computation of supercritical open-channel flows at a combining junction. In such situations, the network system is composed of channel segments arranged in a branching configuration, with individual channel segments connected at a junction. Therefore, two important issues have to be addressed: (a) the numerical solution in branches, and (b) the internal boundary conditions treatment at the junction. Going from the advantageous literature supports of RKDG methods to a particular investigation for a supercritical benchmark, the second-order Runge,Kutta discontinuous Galerkin (RKDG2) scheme is selected to compute the water flow in branches. For the internal boundary handling, we propose a new approach by incorporating the nonlinear model derived from the conservation of the momentum through the junction. The nonlinear junction model was evaluated against available experiments and then applied to compute the junction internal boundary treatment for steady and unsteady flow applications. Finally, a combining flow problem is defined and simulated by the proposed framework and results are illustrated for many choices of junction angles. Copyright © 2007 John Wiley & Sons, Ltd. [source] Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Koen Hillewaert Abstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton,Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd. [source] Sources of water vapour contributing to the Elbe flood in August 2002,A tagging study in a mesoscale modelTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 638 2009H. Sodemann Abstract In this study we investigate the contribution of various moisture sources to the Elbe flood that occurred in Central Europe during August 2002. An 8-day simulation with the mesoscale numerical weather prediction model CHRM, including newly implemented water vapour tracers, has been performed. According to the simulation, rather than drawing moisture from one single dominant source region, water vapour from widely separated moisture sources contributed to the extreme precipitation in the most affected area, notably at distinct, subsequent periods of time, and each in significant amounts. These moisture sources include the Atlantic and Mediterranean ocean areas inside the model domain, evapotranspiration from land areas, and long-range advection from subtropical areas outside the model domain. The results highlight the importance of the concurrent upper-level circulation and the mesoscale flow structures associated with the cyclone for producing extreme precipitation in parts of Germany, Austria, and the Czech Republic during that period. Furthermore, the numerical and technical problems of implementing water vapour tracers into a limited-area model are discussed, including conservative tracer advection, initialization, boundary treatment, and the handling of precipitation parametrizations. An evaluation of the consistency of the method in terms of water vapour, cloud water, and precipitation is provided, with generally satisfying results. The model with its detailed water vapour tracer implementation can now be used for further case-studies and climatological simulations, and serve as a reference for evaluating the performance of other moisture tracking methods, such as those based on backward trajectories. Copyright © 2009 Royal Meteorological Society [source] | ||||||||||