Search results for "Numerical"

Numerical approach to the exact controllability of hyperbolic systems

2005

In this paper we present the numerical implementation of H.U.M. (Hilbert Uniqueness Method, J.L.Lions[1]). We restrict ourselves to the exact boundary controllability of the wave equation, with Dirichlet controls, but the numerical method presented here can be applied to other kinds of controllability. The problem is discretized by a finite elements of first order in space and by a discrete time Galerkin approximation (Dupont [1]). The efficiency of the method is illustrated by numerical results.

2021

Abstract. The formation of ice in clouds is an important processes in mixed-phase and ice-phase clouds. Yet, the representation of ice formation in numerical models is highly uncertain. In the last decade, several new parameterizations for heterogeneous freezing have been proposed. However, it is currently unclear what the effect of choosing one parameterization over another is in the context of numerical weather prediction. We conducted high-resolution simulations (Δx=250 m) of moderately deep convective clouds (cloud top ∼-18 ∘C) over the southwestern United Kingdom using several formulations of ice formation and compared the resulting changes in cloud field properties to the spread of an…

Sea breeze thunderstorms in the eastern Iberian Peninsula. Neighborhood verification of HIRLAM and HARMONIE precipitation forecasts

2014

In this study we investigated sea breeze thunderstorms with intense convective activity (i.e., heavy rainfall, hail and gusty winds) that occurred over the eastern Iberian Peninsula (Spain) and were missed by the operational HIRLAM model. We used two grid-spacing setups (5.0. km and 2.5. km) of the hydrostatic HIRLAM model, and the non-hydrostatic spectral HARMONIE suite (2.5. km), to simulate isolated convection associated with sea breezes. The overall aim is to estimate the ability of these three experimental setups, in particular the HARMONIE model as the forthcoming operational numerical weather prediction in most European Weather Services, to correctly simulate convective precipitation…

Modelling of EM glass convection

2008

PurposeTo develop the mathematical model, which allows predicting the temperature and flow distribution of an opaque glass melt with the temperature‐dependent properties in case it is generated by electromagnetic and thermal convection. Analysis has been done for geometry of the model crucible with the immersed rod electrodes. Numerical analysis is used as a tool for finding out the parameters of the system, which allow getting desiderated homogeneity of temperature field by EM action.Design/methodology/approachANSYS CFX software is implemented for coupling of EM, thermal and HD processes in the modelled system. Usability of non‐inductive approximation is shown using a full harmonic analysi…

Classification of precipitation events with a convective response timescale and their forecasting characteristics

2011

[1] The convective timescale τc, which is mainly determined by the ratio of CAPE and precipitation rate, provides a physically-based measure to distinguish equilibrium and non-equilibrium convection. A statistical analysis of this timescale, based upon observational data from radiosonde ascents, rain gauges, and radar for seven warm seasons in Germany, reveals that the equilibrium and non-equilibrium regimes can be regarded as extremes of a continuous distribution. The two regimes characterize very different interactions between the large-scale flow and convection. The quality of precipitation forecasts from a non-hydrostatic regional weather prediction model with parameterized convection d…

Influence of Skin Depth on Convective Heat Transfer in Induction Heating

2017

International audience; We investigate convection driven by induction heating of a horizontal fluid layer using direct numerical simulations (DNS). This problem is of particular interest in the context of nuclear severe accident mastering. In a real severe accident, the molten core is subjected to homogeneous internal sources resulting from nuclear disintegrations. This situation is mimicked in the laboratory using induction heating as the internal source. In induction heating, however, heat sources are localized in the skin layer. Consequently, this concentration of heat may modify the flow and wall heat transfer compared to the case of homogeneous internal sources. DNS are carried out for…

Influence of growth parameters and melt convection on the solid-liquid interface during RF-floating zone crystal growth of intermetallic compounds

2001

Abstract The influence of growth parameters and melt convection on the solid–liquid interface of the intermetallic compound Ni3Si grown by the RF-floating zone technique was investigated experimentally as well as numerically. Numerical simulations showed that the heat transfer is strongly influenced by the electromagnetically driven and Marangoni convections whereas both the buoyancy and feed rotation have a negligible effect. It was found experimentally that the inductor design, the rod diameter and the length of the molten zone influence the solid–liquid interface shape significantly. The electromagnetically driven convection increases dramatically with increasing zone length due to the r…

Fronts propagating with signal dependent speed in limited diffusion and related Hamilton-Jacobi formulations

2021

We consider a class of limited diffusion equations and explore the formation of diffusion fronts as the result of a combination of diffusive and hyperbolic transport. We analyze a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion coefficient that depends on the unknown and on the gradient of the unknown. We explore the main features of the solution of the Hamilton-Jacobi equations that contain shocks and propose a suitable numerical scheme that approximates the solution in a consistent way with respect to the solution of the associated Fokker-Planck equation. We analyze three model problems covering d…

Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography

2018

Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…

Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations

1985

Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.