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semi-Lagrangian Scheme (semi-lagrangian + scheme)

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Engineering25%

Selected Abstracts

Simplified model for mould filling simulations using CVFEM and unstructured meshes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2007
K. C. Estacio
Abstract In this work, the finite volume method is used to numerically solve the fluid governing equations of the filling phase of thermoplastic injection in a narrow gap with free surfaces, subject to heat transfer, using a semi-Lagrangian formulation in an unstructured mesh. The modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of the melt. The pressure field is obtained using the control volume finite element method. The three-dimensional temperature field is solved by a semi-Lagrangian scheme based on the finite volume method. A simpler two-dimensional model for temperature field is also deduced and presented. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surface

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005
Leo Miguel González Gutiérrez
Abstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Coupling a mass-conserving semi-Lagrangian scheme (SLICE) to a semi-implicit discretization of the shallow-water equations: Minimizing the dependence on a reference atmosphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 646 2010
J. Thuburn
Abstract In a recent paper, a conservative semi-Lagrangian mass transport scheme SLICE has been coupled to a semi-implicit semi-Lagrangian scheme for the shallow-water equations. The algorithm involves the solution at each timestep of a nonlinear Helmholtz problem, which is achieved by iterative solution of a linear ,inner' Helmholtz problem; this framework, as well as the linear Helmholtz operator itself, are the same as would be used with a non-conservative interpolating semi-Lagrangian scheme for mass transport. However, in order to do this, a reference value of geopotential was introduced into the discretization. It is shown here that this results in a weak dependence of the results on that reference value. An alternative coupling is therefore proposed that preserves the same solution framework and linear Helmholtz operator but, at convergence of the nonlinear solver, has no dependence on the reference value. However, in order to maintain accuracy at large timesteps, this approach requires a modification to how SLICE performs its remapping. An advantage of removing the dependence on the reference value is that the scheme then gives consistent tracer transport. Copyright © 2010 Royal Meteorological Society and Crown Copyright. Published by John Wiley & Sons, Ltd. [source]

A monotonic and positive,definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 611 2005
Mohamed Zerroukat
Abstract A new monotonic and positive,definite filter is incorporated into an existing Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme for transport problems in both Cartesian and spherical geometry. The SLICE scheme is based on a control-volume approach that uses multiple sweeps of a one-dimensional O (,x4) conservation remapping algorithm along predetermined cascade directions. The new filter combines a selective detection algorithm, to pinpoint regions of non-monotonic behaviour, with a hierarchical reduction of the degree of the piecewise reconstruction in such regions, to re-establish monotonicity. The enhanced, monotonic and positive,definite, SLICE scheme is tested in one dimension, and then applied to standard two-dimensional test problems in both Cartesian and spherical geometries. Comparisons with published results of other conservative semi-Lagrangian schemes show that it performs well. © Crown copyright, 2005. [source]

SLICE-S: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems on the Sphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 602 2004
Mohamed Zerroukat
Abstract The Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme developed for Cartesian geometry is generalized to spherical geometry. The spherical version, SLICE-S, is similarly based on a Control Volume approach and multiple sweeps of a one-dimensional O(,s4) (where s is the spherical distance) conservative remapping algorithm along Eulerian latitudes, then along Lagrangian longitudes. The resulting conservative scheme requires no restriction on either the polar meridional or zonal Courant numbers. SLICE-S is applied to the standard problems of solid-body rotation and deformational flow, and results are compared with those of a standard non-conservative and other published conservative semi-Lagrangian schemes. In addition to mass conservation, and consistent with the performance of SLICE, the present scheme is competitive in terms of accuracy and efficiency. © Crown copyright, 2004. Royal Meteorological Society [source]

Instability in a class of explicit two-time-level semi-Lagrangian schemes

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 596 2004
Dale R. Durran
Abstract Recently Gospodinov and collaborators derived a family of second-order two-time-level semi-Lagrangian schemes that contain an undetermined parameter ,. It is shown that, when using one of these schemes to approximate the forcing terms in partial differential equations in a semi-Lagrangian coordinate frame, the choice of , has a critical influence on the absolute stability of the method. Optimal stability properties are obtained by choosing , = ¼ which corresponds to the SETTLS scheme proposed by Hortal. Copyright © 2004 Royal Meteorological Society [source]