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Advection Term
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J. Dünnermann – One of the best experts on this subject based on the ideXlab platform.

Estimation of the Advection effects induced by surface heterogeneities in the surface energy budget
Atmospheric Chemistry and Physics, 2016CoAuthors: J. Cuxart, B. Wrenger, D. Martínezvillagrasa, J. Reuder, M.o. Jonassen, M.a. Jiménez, M. Lothon, F. Lohou, O. Hartogensis, J. DünnermannAbstract:Abstract. The effect of terrain heterogeneities in onepoint measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the Advection Term in the equation of the evolution of temperature as generated by documented terrain heterogeneities and we estimate its importance as a Term in the surface energy budget (SEB), for which the turbulent fluxes are computed using the eddycorrelation method. The heterogeneities are estimated from satellite and model fields for scales near 1 km or broader, while the smaller scales are estimated through direct measurements with remotely piloted aircraft and thermal cameras and also by highresolution modelling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the Advection Term becomes more important as the scales become finer. The Advection Term provides nonsignificant values to the SEB at scales larger than a few kilometres. In contrast, surface heterogeneities at the metre scale yield large values of the Advection, which are probably only significant in the first centimetres above the ground. The motions that seem to contribute significantly to the Advection Term in the SEB equation in our case are roughly those around the hectometre scales.

Estimation of the Advection effects induced by surface heterogeneities in the surface energy budget
, 2016CoAuthors: J. Cuxart, B. Wrenger, D. Martínezvillagrasa, J. Reuder, M.o. Jonassen, M.a. Jiménez, M. Lothon, F. Lohou, O. Hartogensis, J. DünnermannAbstract:Abstract. The effect of terrain heterogeneities in onepoint measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the Advection Term in the equation of the temperature as generated by documented terrain heterogeneities and we estimate its importance as a Term in the surface energy budget (SEB). The heterogeneities are estimated from satellite and model fields for scales near 1 kilometer or broader, while the smaller scales are estimated through direct measurements with remotelypiloted aircraft, thermal cameras and also by highresolution modeling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the Advection Term becomes more important as the scales become finer. The Advection Term provides nonsignificant values to the SEB at scales larger than few kilometers. On the contrary, surface heterogeneities at the meter scale yield large values of the Advection, which are probably only significant in the first centimeters above the ground. The motions that seem to contribute significantly to the Advection Term in the SEB equation in our case are roughly those around the hectometer scales.
Akio Arakawa – One of the best experts on this subject based on the ideXlab platform.

computational design for long Term numerical integration of the equations of fluid motion
Journal of Computational Physics, 1997CoAuthors: Akio ArakawaAbstract:The integral constraints on quadratic quantities of physical importance, such as conservation of mean kinetic energy and mean square vorticity, will not be maintained in finite difference analogues of the equation of motion for twodimensional incompressible flow, unless the finite difference Jacobian expression for the Advection Term is restricted to a form which properly represents the interaction between grid points, as derived in this paper. It is shown that the derived form of the finite difference Jacobian prevents nonlinear computational instability and thereby permits longTerm numerical integrations.

Computational design for longTerm numerical integration of the equations of fluid motion: Twodimensional incompressible flow. Part I☆
Journal of Computational Physics, 1997CoAuthors: Akio ArakawaAbstract:Abstract The integral constraints on quadratic quantities of physical importance, such as conservation of mean kinetic energy and mean square vorticity, will not be maintained in finite difference analogues of the equation of motion for twodimensional incompressible flow, unless the finite difference Jacobian expression for the Advection Term is restricted to a form which properly represents the interaction between grid points, as derived in this paper. It is shown that the derived form of the finite difference Jacobian prevents nonlinear computational instability and thereby permits longTerm numerical integrations.
Karol Mikula – One of the best experts on this subject based on the ideXlab platform.

Design and analysis of finite volume methods for elliptic equations with oblique derivatives; application to Earth gravity field modelling
Journal of Computational Physics, 2019CoAuthors: Jérôme Droniou, Matej Medl’a, Karol MikulaAbstract:Abstract We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not assumed to have a specific form, but only to satisfy some (usual) coercivity and consistency properties. The oblique boundary conditions are split into a normal component, which directly appears in the flux balance on control volumes touching the domain boundary, and a tangential component which is managed as an Advection Term on the boundary. This Advection Term is discretised using a finite volume method based on a centred discretisation (to ensure optimal rates of convergence) and stabilised using a vanishing boundary viscosity. A convergence analysis, based on the 3rd Strang Lemma [9] , is conducted in this generic finite volume framework, and yields the expected O ( h ) optimal convergence rate in discrete energy norm. We then describe a specific choice of numerical fluxes, based on a generalised hexahedral meshing of the computational domain. These fluxes are a corrected version of fluxes originally introduced in [29] . We identify mesh regularity parameters that ensure that these fluxes satisfy the required coercivity and consistency properties. The theoretical rates of convergence are illustrated by an extensive set of 3D numerical tests, including some conducted with two variants of the proposed scheme. A test involving realworld data measuring the disturbing potential in Earth gravity modelling over Slovakia is also presented.

Semiimplicit Second Order Accurate Finite Volume Method for AdvectionDiffusion Level Set Equation
Finite Volumes for Complex Applications VIIElliptic Parabolic and Hyperbolic Problems, 2014CoAuthors: Martin Balažovjech, Peter Frolkovič, Richard Frolkovič, Karol MikulaAbstract:We present a second order accurate finite volume method for level set equation describing the motion in normal direction with the speed depending on external properties and curvature. A convenient combination of a CrankNicolson type of the time discretization for diffusion Term [1] and an Inflow Implicit and Outflow Explicit scheme [6] for Advection Term is used. Numerical experiments for an example with the exact solution derived in this paper and for examples motivated by modeling of fire propagation in forests are presented.
Laurent Gremillet – One of the best experts on this subject based on the ideXlab platform.

Stability of nonlinear VlasovPoisson equilibria through spectral deformation and FourierHermite expansion.
Physical review. E Statistical nonlinear and soft matter physics, 2011CoAuthors: Evangelos Siminos, Didier Bénisti, Laurent GremilletAbstract:We study the stability of spatially periodic, nonlinear VlasovPoisson equilibria as an eigenproblem in a FourierHermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the Advection Term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the Advection Term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic BernsteinGreeneKruskal mode with multiple phasespace vortices, compare our results with numerical simulations of the VlasovPoisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.
J. Cuxart – One of the best experts on this subject based on the ideXlab platform.

Estimation of the Advection effects induced by surface heterogeneities in the surface energy budget
Atmospheric Chemistry and Physics, 2016CoAuthors: J. Cuxart, B. Wrenger, D. Martínezvillagrasa, J. Reuder, M.o. Jonassen, M.a. Jiménez, M. Lothon, F. Lohou, O. Hartogensis, J. DünnermannAbstract:Abstract. The effect of terrain heterogeneities in onepoint measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the Advection Term in the equation of the evolution of temperature as generated by documented terrain heterogeneities and we estimate its importance as a Term in the surface energy budget (SEB), for which the turbulent fluxes are computed using the eddycorrelation method. The heterogeneities are estimated from satellite and model fields for scales near 1 km or broader, while the smaller scales are estimated through direct measurements with remotely piloted aircraft and thermal cameras and also by highresolution modelling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the Advection Term becomes more important as the scales become finer. The Advection Term provides nonsignificant values to the SEB at scales larger than a few kilometres. In contrast, surface heterogeneities at the metre scale yield large values of the Advection, which are probably only significant in the first centimetres above the ground. The motions that seem to contribute significantly to the Advection Term in the SEB equation in our case are roughly those around the hectometre scales.

Estimation of the Advection effects induced by surface heterogeneities in the surface energy budget
, 2016CoAuthors: J. Cuxart, B. Wrenger, D. Martínezvillagrasa, J. Reuder, M.o. Jonassen, M.a. Jiménez, M. Lothon, F. Lohou, O. Hartogensis, J. DünnermannAbstract:Abstract. The effect of terrain heterogeneities in onepoint measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the Advection Term in the equation of the temperature as generated by documented terrain heterogeneities and we estimate its importance as a Term in the surface energy budget (SEB). The heterogeneities are estimated from satellite and model fields for scales near 1 kilometer or broader, while the smaller scales are estimated through direct measurements with remotelypiloted aircraft, thermal cameras and also by highresolution modeling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the Advection Term becomes more important as the scales become finer. The Advection Term provides nonsignificant values to the SEB at scales larger than few kilometers. On the contrary, surface heterogeneities at the meter scale yield large values of the Advection, which are probably only significant in the first centimeters above the ground. The motions that seem to contribute significantly to the Advection Term in the SEB equation in our case are roughly those around the hectometer scales.