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Advection Scheme (advection + scheme)
Selected AbstractsPhysically-based Dye Advection for Flow VisualizationCOMPUTER GRAPHICS FORUM, Issue 3 2008Guo-Shi Li Abstract Dye advection is widely used in experimental flow analysis but has seen less use for visualization in computational fluid dynamics. One possible reason for this disconnect is the inaccuracy of the texture-based approach, which is prone to artifacts caused by numeric diffusion and mass fluctuation. In this paper, we introduce a novel 2D dye advection scheme for flow visualization based on the concept of control volume analysis typically used in computational fluid dynamics. The evolution of dye patterns in the flow field is achieved by advecting individual control volumes, which collectively cover the entire spatial domain. The local variation of dye material, represented as a piecewise quasi-parabolic function, is integrated within each control volume resulting in mass conserving transport without excessive numerical diffusion. Due to its physically based formulation, this approach is capable of conveying intricate flow structures not shown in the traditional dye advection schemes while avoiding visual artifacts. [source] First experience of compressible gas dynamics simulation on the Los Alamos roadrunner machineCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 17 2009Paul R. Woodward Abstract We report initial experience with gas dynamics simulation on the Los Alamos Roadrunner machine. In this initial work, we have restricted our attention to flows in which the flow Mach number is less than 2. This permits us to use a simplified version of the PPM gas dynamics algorithm that has been described in detail by Woodward (2006). We follow a multifluid volume fraction using the PPB moment-conserving advection scheme, enforcing both pressure and temperature equilibrium between two monatomic ideal gases within each grid cell. The resulting gas dynamics code has been extensively restructured for efficient multicore processing and implemented for scalable parallel execution on the Roadrunner system. The code restructuring and parallel implementation are described and performance results are discussed. For a modest grid size, sustained performance of 3.89 Gflops,1 CPU-core,1 is delivered by this code on 36 Cell processors in 9 triblade nodes of a single rack of Roadrunner hardware. Copyright © 2009 John Wiley & Sons, Ltd. [source] A second order discontinuous Galerkin method for advection on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2003H. J. M. Geijselaers Abstract In this paper the advection of element data which are linearly distributed inside the elements is addressed. Across element boundaries the data are assumed discontinuous. The equations are discretized by the Discontinuous Galerkin method. For stability and accuracy at large step sizes (large values of the Courant number), the method is extended to second order. Furthermore the equations are enriched with selective implicit terms. This results in an explicit and local advection scheme, which is stable and accurate for Courant numbers less than .95 on unstructured triangle meshes. Results are shown of some pure advection test problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] Depth-integrated, non-hydrostatic model for wave breaking and run-upINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yoshiki Yamazaki Abstract This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd. [source] Reducing numerical diffusion in interfacial gravity wave simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005O. B. Fringer Abstract We demonstrate how the background potential energy is an excellent measure of the effective numerical diffusion or antidiffusion of an advection scheme by applying several advection schemes to a standing interfacial gravity wave. All existing advection schemes do not maintain the background potential energy because they are either diffusive, antidiffusive, or oscillatory. By taking advantage of the compressive nature of some schemes, which causes a decrease in the background potential energy, and the diffusive nature of others, which causes an increase in the background potential energy, we develop two background potential energy preserving advection schemes that are well-suited to study interfacial gravity waves at a density interface between two miscible fluids in closed domains such as lakes. The schemes employ total variation diminishing limiters and universal limiters in which the limiter is a function of both the upwind and local gradients as well as the background potential energy. The effectiveness of the schemes is validated by computing a sloshing interfacial gravity wave with a nonstaggered-grid Boussinesq solver, in which QUICK is employed for momentum and the pressure correction method is used, which is second-order accurate in time. For scalar advection, the present background potential energy preserving schemes are employed and compared to other TVD and non-TVD schemes, and we demonstrate that the schemes can control the change in the background potential energy due to numerical effects. Copyright © 2005 John Wiley & Sons, Ltd. [source] Flow and mass transfer of fully resolved bubbles in non-Newtonian fluidsAICHE JOURNAL, Issue 7 2007Stefan Radl Abstract In this work, high-resolution 2-D numerical simulations were performed on the motion of deformable bubbles in non-Newtonian fluids and the associated mass transfer. For that purpose, we have implemented a semi-Lagrangian advection scheme and improved the fluid dynamic calculation by the usage of implicit algorithms. Non-Newtonian fluids are described by generalized Newtonian as well as viscoelastic model fluids. As shear-thinning model we use a Power-Law and a Carreau-Yasuda model, the viscoelastic fluid simulations are based on an Upper-Convected Maxwell model combined with a recently introduced model for the evolution of the effective shear rate. The mathematical challenges arising from the hyperbolic nature of the resulting set of equations are addressed by inclusion of artificial diffusion in the stress equation. In our work, it was found that shear thinning effects have impact on collision rates, and therefore, may influence coalescence of bubbles in non-Newtonian liquids. Furthermore, for the first time, concentration fields of dissolved gas in viscoelastic fluids are presented. The study shows that the fluid elasticity plays a major role for bubble rise velocity, and therefore, mass transfer. As the wake dynamics differ significantly from that in Newtonian liquids, abnormal mixing characteristics can be expected in the bubbly flow of viscoelastic fluids. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] The local ETKF and SKEB: Upgrades to the MOGREPS short-range ensemble prediction systemTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 640 2009Neill E. Bowler Abstract The Met Office has been routinely running a short-range global and regional ensemble prediction system (EPS) since the summer of 2005. This article describes a major upgrade to the global ensemble, which affected both the initial condition and model uncertainty perturbations applied in that ensemble. The change to the initial condition perturbations is to allow localization within the ensemble transform Kalman filter (ETKF). This enables better specification of the ensemble spread as a function of location around the globe. The change to the model uncertainty perturbations is the addition of a stochastic kinetic energy backscatter scheme (SKEB). This adds vorticity perturbations to the forecast in order to counteract the damping of small-scale features introduced by the semi-Lagrangian advection scheme. Verification of ensemble forecasts is presented for the global ensemble system. It is shown that the localization of the ETKF gives a distribution of the spread as a function of latitude that better matches the forecast error of the ensemble mean. The SKEB scheme has a substantial effect on the power spectrum of the kinetic energy, and with the scheme a shallowing of the spectral slope is seen in the tail. A k,5/3 slope is seen at wavelengths shorter than 1000 km and this better agrees with the observed spectrum. The local ETKF significantly improves forecasts at all lead times over a number of variables. The SKEB scheme increases the rate of growth of ensemble spread in some variables, and improves forecast skill at short lead times. ©Crown Copyright 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd. [source] Semi-Lagrangian advection scheme with controlled damping: An alternative to nonlinear horizontal diffusion in a numerical weather prediction modelTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 631 2008Filip Vá Abstract This paper proposes a nonlinear horizontal diffusion scheme for models using semi-Lagrangian formulations. The scheme is made flow dependent and not entirely linked to the model levels. As an extension, the implementation of the scheme to the model Aladin is given. The damping abilities of interpolation are used for the diffusion filtering. The aim is to provide a horizontal diffusion scheme of similar stability and computational efficiency as the existing linear spectral diffusion scheme in Aladin. Preserving such qualities, the new scheme brings beneficial new skills to the model. The differences between the performances of the two diffusion schemes are examined and discussed. Finally, some interesting case-studies simulated with both horizontal diffusion schemes are presented. Copyright © 2008 Royal Meteorological Society [source] Eulerian backtracking of atmospheric tracers.THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 615 2006II: Numerical aspects Abstract In Part I of this paper, a mathematical equivalence was established between Eulerian backtracking or retro- transport, on the one hand, and adjoint transport with respect to an air-mass-weighted scalar product, on the other. The time symmetry which lies at the basis of this mathematical equivalence can however be lost through discretization. That question is studied, and conditions are explicitly identified under which discretization schemes possess the property of time symmetry. Particular consideration is given to the case of the LMDZ model. The linear schemes used for turbulent diffusion and subgrid-scale convection are symmetric. For the Van Leer advection scheme used in LMDZ, which is nonlinear, the question of time symmetry does not even make sense. Those facts are illustrated by numerical simulations performed in the conditions of the European Transport EXperiment (ETEX). For a model that is not time-symmetric, the question arises as to whether it is preferable, in practical applications, to use the exact numerical adjoint, or the retro-transport model. Numerical results obtained in the context of one-dimensional advection show that the presence of slope limiters in the Van Leer advection scheme can produce in some circumstances unrealistic (in particular, negative) adjoint sensitivities. The retro-transport equation, on the other hand, generally produces robust and realistic results, and always preserves the positivity of sensitivities. Retro-transport may therefore be preferable in sensitivity computations, even in the context of variational assimilation. Copyright © 2006 Royal Meteorological Society [source] Physically-based Dye Advection for Flow VisualizationCOMPUTER GRAPHICS FORUM, Issue 3 2008Guo-Shi Li Abstract Dye advection is widely used in experimental flow analysis but has seen less use for visualization in computational fluid dynamics. One possible reason for this disconnect is the inaccuracy of the texture-based approach, which is prone to artifacts caused by numeric diffusion and mass fluctuation. In this paper, we introduce a novel 2D dye advection scheme for flow visualization based on the concept of control volume analysis typically used in computational fluid dynamics. The evolution of dye patterns in the flow field is achieved by advecting individual control volumes, which collectively cover the entire spatial domain. The local variation of dye material, represented as a piecewise quasi-parabolic function, is integrated within each control volume resulting in mass conserving transport without excessive numerical diffusion. Due to its physically based formulation, this approach is capable of conveying intricate flow structures not shown in the traditional dye advection schemes while avoiding visual artifacts. [source] Reducing numerical diffusion in interfacial gravity wave simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005O. B. Fringer Abstract We demonstrate how the background potential energy is an excellent measure of the effective numerical diffusion or antidiffusion of an advection scheme by applying several advection schemes to a standing interfacial gravity wave. All existing advection schemes do not maintain the background potential energy because they are either diffusive, antidiffusive, or oscillatory. By taking advantage of the compressive nature of some schemes, which causes a decrease in the background potential energy, and the diffusive nature of others, which causes an increase in the background potential energy, we develop two background potential energy preserving advection schemes that are well-suited to study interfacial gravity waves at a density interface between two miscible fluids in closed domains such as lakes. The schemes employ total variation diminishing limiters and universal limiters in which the limiter is a function of both the upwind and local gradients as well as the background potential energy. The effectiveness of the schemes is validated by computing a sloshing interfacial gravity wave with a nonstaggered-grid Boussinesq solver, in which QUICK is employed for momentum and the pressure correction method is used, which is second-order accurate in time. For scalar advection, the present background potential energy preserving schemes are employed and compared to other TVD and non-TVD schemes, and we demonstrate that the schemes can control the change in the background potential energy due to numerical effects. Copyright © 2005 John Wiley & Sons, Ltd. [source] Semi-analytical method for departure point determinationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005Nick Martin Abstract A new method for departure point determination on Cartesian grids, the semi-analytical upwind path line tracing (SUT) method, is presented and compared to two typical departure point determination methods used in semi-Lagrangian advection schemes, the Euler method and the four-step Runge,Kutta method. Rigorous comparisons of the three methods were conducted for a severely curving hypothetical flow field and for advective transport in the rotation of a Gaussian concentration hill. The SUT method was shown to have equivalent accuracy to the Runge,Kutta method but with significantly improved computational efficiency. Depending on the case being simulated, the SUT method provides either far greater or equivalent computational efficiency and more certain accuracy than the Euler method. Copyright © 2004 John Wiley & Sons, Ltd. [source] Consistency with continuity in conservative advection schemes for free-surface modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2002Edward S. Gross Abstract The consistency of the discretization of the scalar advection equation with the discretization of the continuity equation is studied for conservative advection schemes coupled to three-dimensional flows with a free-surface. Consistency between the discretized free-surface equation and the discretized scalar transport equation is shown to be necessary for preservation of constants. In addition, this property is shown to hold for a general formulation of conservative schemes. A discrete maximum principle is proven for consistent upwind schemes. Various numerical examples in idealized and realistic test cases demonstrate the practical importance of the consistency with the discretization of the continuity equation. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||