Computer Methods in Applied Mechanics and Engineering, Sep 1, 1996
Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order fin... more Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure.
Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has represent... more Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. In this lagrangian version of the model, the computational ...
In recent years, unstructured-mesh models have gained attention due to their flexibility in repre... more In recent years, unstructured-mesh models have gained attention due to their flexibility in representing complex topography and variable spatial resolution. The Second generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim) is an unstructured-mesh finite element model that is being developed at the Universite catholique de Louvain (Louvain-la-Neuve, Belgium). The ocean model solves the shallow water equations by means of the discontinuous Galerkin finite element method. It features a 1D river model, 2D depth averaged model and a full 3D model. After a general presentation of SLIM and its main applications, we will further focus on sea-ice modeling. The sea-ice component of SLIM has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. Such an example is illustrated by the numerous narrow straits constituting the Canadian Arctic Archipelago. A key point of unstructured meshes is that they allow the use of mesh adaptivity. A Lagrangian, adaptive sea ice model allowing the computational grid to move with the ice drift is currently being developed. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. This Lagrangian version of the model has several interesting applications, such as the dynamical mesh refinement along any region of interest (e.g., the ice edge), buoys tracking, or the inclusion of material properties in the rheology. Among these applications, the ice age constitutes both an interesting diagnostic tool and parameter for determining the ice physical properties (albedo, strength, salinity, ...). There are basically two ways of modeling the ice age: as a bidimensional tracer or as a vertical tracer, but different definitions exist and lead to different interpretations. In this work, we first present the equation of evolution of the age in an onedimensional ice layer. This equation is applied to a stand-alone thermodynamic sea ice model and its numerical resolution is compared to the integration of the ice age thanks to Lagrangian particles in the vertical direction. Preliminary results of a simulation of the Arctic Basin are finally shown where the Lagrangian model is used to transport the vertical structure of ice age
The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals wi... more The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals with the equations governing sea-ice, geophysical, environmental and groundwater phenomena by means of the (discontinuous Galerkin) finite element method on 1D, 2D or 3D unstructured meshes. To take advantage of state-of-the-art developments, SLIM is also being interfaced with existing tools (often based on radically different numerical methods), such as the well-known and widely used General Ocean Turbulence Model (www.gotm.net, GOTM). The post-processing of the results is achieved with the help of usual statistical and computer graphics methods. Other techniques are also resorted to, such as tracer and timescale methods derived from CART (Constituent-oriented Age and Residence time Theory, www.climate.be/cart) or network science tools (sites.uclouvain.be/networks) (Thomas et al. 2014).The hydrodynamics simulated by the aforementioned finite element model can be introduced into a number of SLIM-based environmental modules, which are capable of representing sediment transport (Delandmeter et al. 2015), as well as the fate of some classes of contaminants, namely microbiological pollutants (de Brauwere et al. 2014), endocrine disrupting compounds, heavy metals (Elskens et al. 2014) or radionuclides. A simple ecological model is being developed, whose aim is to simulate the evolution of various species of phyto- and zoo-plankton (Naithani et al. 2016).
Computer Methods in Applied Mechanics and Engineering, Sep 1, 1996
Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order fin... more Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure.
Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has represent... more Abstract We present a lagrangian, finite element, adaptive sea-ice model. Our model has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. In this lagrangian version of the model, the computational ...
In recent years, unstructured-mesh models have gained attention due to their flexibility in repre... more In recent years, unstructured-mesh models have gained attention due to their flexibility in representing complex topography and variable spatial resolution. The Second generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim) is an unstructured-mesh finite element model that is being developed at the Universite catholique de Louvain (Louvain-la-Neuve, Belgium). The ocean model solves the shallow water equations by means of the discontinuous Galerkin finite element method. It features a 1D river model, 2D depth averaged model and a full 3D model. After a general presentation of SLIM and its main applications, we will further focus on sea-ice modeling. The sea-ice component of SLIM has representations of both dynamic and thermodynamic sea-ice processes and includes viscous-plastic rheology along with a complete parametrization of the atmospheric fluxes. Unstructured meshes, with their natural ability to fit boundaries and increase locally the mesh resolution, propose an alternative framework to capture the complex oceanic areas formed by coasts and islands. Such an example is illustrated by the numerous narrow straits constituting the Canadian Arctic Archipelago. A key point of unstructured meshes is that they allow the use of mesh adaptivity. A Lagrangian, adaptive sea ice model allowing the computational grid to move with the ice drift is currently being developed. In order to maintain a good quality of the mesh, the mesh has to be adapted during the simulation, involving particular mesh adaptation techniques. This Lagrangian version of the model has several interesting applications, such as the dynamical mesh refinement along any region of interest (e.g., the ice edge), buoys tracking, or the inclusion of material properties in the rheology. Among these applications, the ice age constitutes both an interesting diagnostic tool and parameter for determining the ice physical properties (albedo, strength, salinity, ...). There are basically two ways of modeling the ice age: as a bidimensional tracer or as a vertical tracer, but different definitions exist and lead to different interpretations. In this work, we first present the equation of evolution of the age in an onedimensional ice layer. This equation is applied to a stand-alone thermodynamic sea ice model and its numerical resolution is compared to the integration of the ice age thanks to Lagrangian particles in the vertical direction. Preliminary results of a simulation of the Arctic Basin are finally shown where the Lagrangian model is used to transport the vertical structure of ice age
The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals wi... more The Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM, www.climate.be/slim_flyer) deals with the equations governing sea-ice, geophysical, environmental and groundwater phenomena by means of the (discontinuous Galerkin) finite element method on 1D, 2D or 3D unstructured meshes. To take advantage of state-of-the-art developments, SLIM is also being interfaced with existing tools (often based on radically different numerical methods), such as the well-known and widely used General Ocean Turbulence Model (www.gotm.net, GOTM). The post-processing of the results is achieved with the help of usual statistical and computer graphics methods. Other techniques are also resorted to, such as tracer and timescale methods derived from CART (Constituent-oriented Age and Residence time Theory, www.climate.be/cart) or network science tools (sites.uclouvain.be/networks) (Thomas et al. 2014).The hydrodynamics simulated by the aforementioned finite element model can be introduced into a number of SLIM-based environmental modules, which are capable of representing sediment transport (Delandmeter et al. 2015), as well as the fate of some classes of contaminants, namely microbiological pollutants (de Brauwere et al. 2014), endocrine disrupting compounds, heavy metals (Elskens et al. 2014) or radionuclides. A simple ecological model is being developed, whose aim is to simulate the evolution of various species of phyto- and zoo-plankton (Naithani et al. 2016).
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