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Erick Carlier - One of the best experts on this subject based on the ideXlab platform.

  • Total variation diminishing schemes for pollutant transport in porous media
    Hydrological Processes, 2008
    Co-Authors: Lahcen Zouhri, Hassam Smaoui, Erick Carlier
    Abstract:

    A bidimensional numerical model has been used in order to simulate the contaminant transport in the coastal groundwater area (Atlantic margin of the Rharb basin, Morocco). This groundwater is materialized by means of the salt contamination derived from several factors: evapotranspiration, lithological series formations, marine intrusion, and processes of interaction between water and rocks. In order to reduce the numerical diffusion and limit the numerical dispersion, we use the Superbee Flux Limiter as a total variation diminishing scheme to discretize the convective operator. This kind of discretization was applied to the coastal groundwater of the Rharb basin (Morocco). The results show that the Superbee Flux Limiter is efficient at drawing the path of the contaminant front with high accuracy. Consequently, this scheme could constitute an approach in water management and allows one to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective.

Francisco Chinesta - One of the best experts on this subject based on the ideXlab platform.

  • an efficient solver of the saturation equation in liquid composite molding processes
    International Journal of Material Forming, 2010
    Co-Authors: J A Garcia, Francisco Chinesta, Ll Gascon, Edu Ruiz, François Trochu
    Abstract:

    A major issue in Liquid Composite Molding Process (LCM) concerns the reduction of voids formed during the resin filling process. Reducing the void content increases the quality of the composite and improves its mechanical properties. Most of modeling efforts on process simulation of mold filling has been focused on the single phase Darcy’s law, with resin as the only phase, ignoring the formation and transport of voids. The resin flow in a partially saturated region can be characterized as two phase flow through a porous medium. The mathematical formulation of saturation in LCM takes into account the interaction between resin and air as it occurs in a two phase flow. This model leads to the introduction of relative permeabilities as a function of saturation. The modified saturation equation is obtained as a result, which is a non-linear advection-diffusion equation with viscous and capillary phenomena. In this work, a Flux Limiter technique has been used to solve a modified saturation equation for the LCM process. The implemented algorithm allows a numerical optimization of the injected flow rate which minimizes the micro/macroscopic void formation during mold filling. Some preliminary numerical results are presented here in order to validate the proposed mathematical model and the numerical scheme. This formulation opens up new opportunities to improve LCM flow simulations and optimize injection molds.

  • A Flux Limiter strategy for solving the saturation equation in resin transfer molding process simulation
    Composites Part A: Applied Science and Manufacturing, 2010
    Co-Authors: Juan Antonio Garcia, Ll Gascon, Francisco Chinesta
    Abstract:

    The main aim of this work is to propose a numerical procedure for solving the saturation equation in RTM process simulation. In order to analyze in more detail the progressive impregnation of a fibrous preform by a fluid resin, the numerical model proposed here considers the flow through a partially saturated medium, including the dependence of permeability on the saturation degree. The model consists of an elliptic equation governing the pressure distribution and a transport hyperbolic equation describing the evolution of the saturation in RTM. A global Flux Limiter fixed mesh strategy is proposed for solving the transport equation with a source term. The Flux Limiter method has the ability to limit the extra numerical diffusion introduced by standard first-order schemes. This formulation can lead to improvements of existing RTM flow simulation codes and optimize the injection process. Preliminary numerical results are presented to validate this new approach.

  • A Flux Limiter strategy for solving the saturation equation in RTM process simulation
    2008
    Co-Authors: Juan Antonio Garcia, Francisco Chinesta, Ll Gascon, François Trochu
    Abstract:

    The main aim of this work is the proposal of a numerical procedure for solving the saturation equation in RTM process simulation. In order to analyze in more detail the progressive impregnation of a fibrous preform by a fluid resin, the numerical model here proposed considers the flow through a partially saturated medium, including the dependence of permeability on the saturation degree. The model consists of an elliptic equation governing the pressure distribution and a transport hyperbolic equation governing the evolution of the saturation. A global Flux Limiter fixed mesh strategy is proposed for solving the transport equation with source term which describes the saturation evolution in RTM process. The Flux Limiter method has the ability to limit the extra numerical diffusion introduced by standard first-order schemes. This formulation could be an appealing choice for improving RTM flow simulations and optimize injection processes. Some preliminary numerical results are presented in order to validate the proposed numerical strategy.

  • Towards an efficient numerical treatment of the transport problems in the resin transfer molding simulation
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: Fernando Sánchez, Juan Antonio Garcia, Llanos Gascón, Francisco Chinesta
    Abstract:

    Efficient liquid composites molding (LCM) processes simulation requires an efficient treatment of the advection equation governing the evolution of different process variables (volume of fluid, heat transfer, incubation time, etc.). In a previous work [J.A. García, Ll. Gascón, F. Chinesta, A fixed mesh numerical method for modelling the flow in liquid composites molding processes using a volume-of-fluid technique, Comput. Methods Appl. Mech. Engrg. 192 (7–8) (2003) 877–893], a second-order scheme with Flux Limiters was proposed for the integration of the advection equation which governs the volume fraction evolution. Due to the fact that other properties, like the incubation time, are not defined in the empty part of the mold, some numerical difficulties are found during the process updating [F. Chinesta, T. Mabrouki, A. Ramón, Some difficulties in the flow front treatment in fixed mesh simulations of composites forming processes, in: 5th ESAFORM Conference on Material Forming, Kracow, 2002, pp. 295–298]. Then the scheme described in García et al. (2003) must be modified to circumvent the difficulty just refereed. This paper describes a new Flux Limiter fixed mesh technique for the calculation of the incubation time and the fluid fraction in mold filling simulation of thin cavities containing a fiber reinforcement. Numerical results in two dimensions are presented in order to validate the proposed numerical strategy.

Lahcen Zouhri - One of the best experts on this subject based on the ideXlab platform.

  • Total variation diminishing schemes for pollutant transport in porous media
    Hydrological Processes, 2008
    Co-Authors: Lahcen Zouhri, Hassam Smaoui, Erick Carlier
    Abstract:

    A bidimensional numerical model has been used in order to simulate the contaminant transport in the coastal groundwater area (Atlantic margin of the Rharb basin, Morocco). This groundwater is materialized by means of the salt contamination derived from several factors: evapotranspiration, lithological series formations, marine intrusion, and processes of interaction between water and rocks. In order to reduce the numerical diffusion and limit the numerical dispersion, we use the Superbee Flux Limiter as a total variation diminishing scheme to discretize the convective operator. This kind of discretization was applied to the coastal groundwater of the Rharb basin (Morocco). The results show that the Superbee Flux Limiter is efficient at drawing the path of the contaminant front with high accuracy. Consequently, this scheme could constitute an approach in water management and allows one to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective.

Eli Turkel - One of the best experts on this subject based on the ideXlab platform.

  • central difference tvd schemes for time dependent and steady state problems
    Journal of Computational Physics, 1993
    Co-Authors: P Jorgenson, Eli Turkel
    Abstract:

    We use central differences to solve the time dependent Euler equations. The schemes are all advanced using a Runge-Kutta formula in time. Near shocks, a second difference is added as an artificial viscosity. This reduces the scheme to a first order upwind scheme at shocks. The switch that is used guarantees that the scheme is locally total variation diminishing (TVD). For steady state problems it is usually advantageous to relax this condition. Then small oscillations do not activate the switches and the convergence to a steady state is improved. To sharpen the shocks, different coefficients are needed for different equations and so a matrix valued dissipation is introduced and compared with the scalar viscosity. The connection between this artificial viscosity and Flux Limiters is shown. Any Flux Limiter can be used as the basis of a shock detector for an artificial viscosity. We compare the use of the van Leer, van Albada, mimmod, superbee, and the 'average' Flux Limiters for this central difference scheme. For time dependent problems, we need to use a small enough time step so that the CFL was less than one even though the scheme was linearly stable for larger time steps. Using a total variation bounded (TVB) Runge-Kutta scheme yields minor improvements in the accuracy.

Hassam Smaoui - One of the best experts on this subject based on the ideXlab platform.

  • Total variation diminishing schemes for pollutant transport in porous media
    Hydrological Processes, 2008
    Co-Authors: Lahcen Zouhri, Hassam Smaoui, Erick Carlier
    Abstract:

    A bidimensional numerical model has been used in order to simulate the contaminant transport in the coastal groundwater area (Atlantic margin of the Rharb basin, Morocco). This groundwater is materialized by means of the salt contamination derived from several factors: evapotranspiration, lithological series formations, marine intrusion, and processes of interaction between water and rocks. In order to reduce the numerical diffusion and limit the numerical dispersion, we use the Superbee Flux Limiter as a total variation diminishing scheme to discretize the convective operator. This kind of discretization was applied to the coastal groundwater of the Rharb basin (Morocco). The results show that the Superbee Flux Limiter is efficient at drawing the path of the contaminant front with high accuracy. Consequently, this scheme could constitute an approach in water management and allows one to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective.