Arbitrary Lagrangian-Eulerian Scheme Research Articles

Coupled pore pressure analysis of cone penetration test in two-layered clay

PurposeThe paper aims to clarify the distribution of excess pore pressure during cone penetration in two-layered clay and its influence on penetrometer resistance.Design/methodology/approachAn arbitrary Lagrangian–Eulerian scheme is adopted to preserve the quality of mesh throughout the numerical simulation. Simplified methods of layered penetration and coupled pore pressure analysis of cone penetration have been proposed and verified by previous studies. The investigation is then extended by the present work to study the cone penetration test in a two-layered clay profile assumed to be homogeneous with the modified Cam clay model.FindingsThe reduction of the range of pore pressure with decreasing PF will cause a decrease of the sensing distance. The PF of the underlying soil is one of the factors that determine the development distance. The interface can be obtained by taking the position of the maximum curvature of the penetrometer resistance curve in the case of stiff clay overlying soft clay. In the case of soft clay overlying stiff clay, the interface locates at the maximum curvature of the penetrometer resistance curve above about 1.6D.Research limitations/implicationsThe cone penetration analyses in this paper are conducted assuming smooth soil-cone contact.Originality/valueA simplified method based on ALE in Abaqus/Explicit is proposed for layered penetration, which solves the problem of mesh distortion at the interface between two materials. The stiffness equivalent method is also proposed to couple pore pressure during cone penetration, which achieves efficient coupling of pore water pressure in large deformations.

Modelling and simulation of surface formation in electrical discharge machining based on thermo-hydraulic coupling

Surface formation in electrical discharge machining (EDM) involves melting, evaporation, re-solidification and crater overlapping. However, almost all existing models concerning surface formation in EDM only consider the thermal process and ignore hydrodynamic phenomena during machining. Herein, a novel three-dimensional thermo-hydraulic coupling model incorporating the arbitrary Lagrangian–Eulerian scheme was developed to address the above problem. The model comprehensively considered the surface deformation caused by melt flow, temperature-dependent material properties, phase changes and the effects of practical forces on melt pools to simulate surface formation on an anodic workpiece at a discharge current of 2 A. Simulation results demonstrate that during single-pulse discharge, molten material flowed radially to the crater periphery. The radial melt flow was driven by evaporation recoil pressure and thermocapillary force. The effect of evaporation recoil pressure on melt flow was gradually counteracted by that of surface tension after discharge ignition, and thermocapillary force became the dominant factor that maintained the existence of bulges around craters. During multiple discharges, the bulges generated by different discharges underwent superposition owing to the flow of molten material and subsequently formed surface peaks. The simulation results also provide the measurements of crater diameter, surface roughness and recast layer thickness, which are consistent with experimental results. The proposed modelling method can provide a useful reference for further investigations on surface integrity in EDM with minimal computing resource requirements.

A dynamic ALE formulation for structures under moving loads

This work describes the implementation of a novel dynamic Arbitrary LagrangianEulerian (ALE) formulation for the simulation of pavement structures loaded by rolling tires in a finite element framework. The proposed formulation enables the simulation of dynamic effects like acceleration, deceleration and variation of the wheel load on the pavement. The ALE scheme is described for a hyperelastic St. Venant-Kirchhoff material capable of finite deformations. With the adoption of this dynamic ALE formulation, a significant improvement in terms of speed and efficiency of the simulation is achieved in comparison to a classical transient Lagrangian formulation. This is primarily because only the relevant portion of the mesh around the applied load needs to be discretized and simulated. Another benefit is that a cumbersome moving load formulation does not need to be implemented. The results show satisfactory agreement with a conventional Lagrangian simulation with a moving load.

Second-Order Time-Accurate ALE Schemes for Flow Computations with Moving and Topologically Changing Grids

In computations of unsteady flow problems by the arbitrary Lagrangian–Eulerian (ALE) method, the introduction of the grid velocity in the transport terms of the governing equations is not a sufficient condition for conservativeness if topology changes in the dynamic mesh are present and the number of mesh cells changes. We discuss an extension to second-order time differencing schemes (Implicit Euler and Crank–Nicolson) in the finite volume framework, to achieve second-order time-accuracy of the solution. Numerical experiments are given to illustrate the effectiveness of the presented method.

Compatible and energy conserving multi-material arbitrary Lagrangian Eulerian scheme for multi-group radiation hydrodynamics simulations

A compatible, bounds preserving and energy conserving multi-material arbitrary Lagrangian Eulerian (ALE) scheme suitable for an unstructured mesh is developed for multi-group radiation hydrodynamics (RHD) simulation of various high energy density physics (HEDP) phenomena involving large material deformations, such as intense thermal radiation or high-power laser driven systems. In order to study very short time scale HEDP phenomena, the electron and ion energy equations (with the effect of electron-ion energy relaxation) are solved separately with an assumption of single macroscopic fluid velocity for each species (two-temperature hydrodynamics model). The governing multi-material hydrodynamics equations are solved by using a higher-order cell-centered hydrodynamics (CCH) scheme. In multi-material flows, the remapping step introduces mixed computational cells in which multiple materials exist in a single cell. Therefore, material interfaces in mixed cells are required to be reconstructed and tracked. In our implementation, this is achieved by using moment-of-fluid (MOF) method. The information of these interfaces is further used to formulate an interface aware sub-scale dynamics (IASSD) scheme for multi-material closure in mixed computational cells. The IASSD scheme is generalized for the two-temperature hydrodynamics model in which separate equations are used to update the electron and ion energies. The multi-group radiation transport on an unstructured mesh is computed using a cell-centered, monotonic, nonlinear finite volume (NLFV) scheme. The flux-limited diffusion (FLD) approximation is used to recover the free-streaming limit of the radiation propagation in optically thin regions. In the ALE step, the electron, ion and radiation energies due to MG-RHD model are conservatively remapped using a center-of-mass (CM) reconstruction of the fields and a compatible and energy conserving remapping scheme. An exact integration based on the intersection between the new (rezoned) and old meshes is used in the remap step. Similar procedure is followed for the remap of cell mass and cell-centered momentum components. In this paper, the details of a compatible, bounds preserving and conservative ALE scheme developed for MG-RHD are described. The remapping of relevant physical quantities due to multi-physics models implemented in the code such as non-local electron energy transport are also discussed. Several validation test problems including laser driven shock propagation in multi-material geometries are provided to demonstrate the accuracy and performance of the ALE scheme implemented.

Comparative analysis of the flow control over a circular cylinder with detached flexible and rigid splitter plates

A comparative study is performed on a circular cylinder with both flexible and rigid splitter plates (SPs). This study has the novelty of using single and dual detached SPs located downstream of the cylinder. The dimensionless gap distance between the first splitter plate and the cylinder as well as the distance between the SPs are varied. The strain of flexible SPs can be used for energy harvesting from the flow. Therefore, a parametric study is performed to find the optimal design for placing piezoelectric polymers. The two-dimensional fluid–structure-interaction analysis is performed based on the arbitrary Lagrangian–Eulerian scheme using COMSOL Multiphysics. Flow characteristics quantities, tip amplitude, and strain are evaluated at different arrangements of the SPs. The results reveal that wake control enhances effectively by doubling the number of SPs. Strain assessments indicate that the strain of dual SPs increases by more than 100% compared to the single plate case. In addition, the amplitude of the dual SPs increases by a remarkable ratio of 18.29 compared to the single plate. In the case of rigid and flexible SPs at a certain arrangement, dramatic reductions of 97.8% and 76.35% in the Strouhal number are obtained compared to a bare cylinder. In addition, 18% drag reduction compared to the bare cylinder is recorded for the rigid SPs. The presented passive method can be used as an attractive approach in flow control as well as energy harvesting from ocean waves and sea currents.

An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations

This paper presents a novel semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using a direct Arbitrary-Lagrangian-Eulerian (ALE) formulation. The scheme is based on a suitable splitting of the governing partial differential equations into subsystems and employs a staggered grid arrangement, where the pressure is defined on the primal simplex mesh, while the velocity and the remaining flow quantities are defined on an edge-based staggered dual mesh. The key idea of the scheme presented in this paper is to discretize the nonlinear convective and viscous terms at the aid of an explicit finite volume scheme that employs the space-time divergence form of the governing equations on moving space-time control volumes. For the convective terms, an ALE extension of the Ducros flux on moving meshes is introduced, which can be proven to be kinetic energy preserving and stable in the energy norm when adding suitable numerical dissipation terms. The use of closed space-time control volumes inside the finite volume scheme guarantees that the important geometric conservation law (GCL) of Lagrangian schemes is verified by construction. Finally, the pressure equation of the Navier-Stokes system is solved on the new mesh configuration at the aid of a classical continuous finite element method, using traditional P1 Lagrange elements.A numerical convergence study confirms that the scheme is second order accurate in space. Subsequently, the ALE hybrid FV/FE method is applied to several incompressible test problems ranging from non-hydrostatic free surface flows over a rising bubble to flows over an oscillating cylinder and an oscillating ellipse. Via the simulation of a circular explosion problem on a moving mesh, we show that the scheme applied to the weakly compressible Navier-Stokes equations is able to capture also weak shock waves, rarefactions and moving contact discontinuities. We also provide numerical evidence which shows that compared to a fully explicit ALE scheme, the semi-implicit ALE method proposed in this paper is particularly efficient for the simulation of weakly compressible flows in the low Mach number limit.

Arbitrary Lagrangian-Eulerian discrete velocity method with application to laser-induced plume expansion

We propose a direct arbitrary Lagrangian-Eulerian (ALE) variant of the previously developed discrete velocity method to solve the kinetic equation with the Bhatnagar–Gross–Krook (BGK) model collision integral. The effectiveness and robustness of the new scheme are demonstrated by computing the axisymmetric plume expansion into a low pressure gas due to evaporation from the solid surface caused by a nanosecond laser pulse. The numerical studies show that the new numerical scheme provides a very significant reduction of the required computing time as compared to the discrete velocity method on a fixed mesh. Cross-comparisons with the direct simulation Monte Carlo (DSMC) approach further confirm the accuracy of the new scheme and model kinetic equations as applied to plume expansion studies. Finally, the good parallel scalability of the new ALE scheme as implemented into the in-house code Nesvetay is demonstrated. The use of two very different approaches to numerical prediction of the transient flow pattern allows us to obtain a reliable numerical solution, which can be regarded as a new transient benchmark test.

Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems

In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic response of the structure is affected greatly by the SFD. In the traditional model, a viscous damping assumption that the damping force is linear with the moving velocity is used. As the nonlinear damping phenomenon is observed for a micro-structure oscillating at a high velocity, this assumption does not hold and will cause error results for predicting the response of the micro-structure. Meanwhile, due to the small size of the device and the low pressure of the encapsulation, the gas in MEMS is usually rarefied gas. Therefore, to correctly predict the damping force, the rarefied gas effect must be considered. To study the nonlinear SFD problem involving the rarefied gas effect, a kinetic method, i.e., discrete unified gas kinetic scheme (DUGKS), is introduced in this paper. Also, based on the DUGKS, two solving methods, i.e., a traditional decoupled method (Eulerian scheme) and a coupled framework (arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods, two basic motion forms, i.e., linear (perpendicular) and tilting motions of a rigid micro-beam, are studied under forced and free oscillations. For a forced oscillation, the nonlinear SFD phenomenon is investigated. For a free oscillation, in the resonance regime, some numerical results at different maximum oscillating velocities are presented and discussed. Besides, the influence of oscillation frequency on the damping force or torque is also studied, and the cause of the nonlinear damping phenomenon is investigated.

Analysis of high Reynolds free surface flows

ABSTRACT In this paper, we will combine an upwind radial basis function-finite element with direct velocity–pressure formulation to study the two-dimensional Navier-Stokes equations with free surface flows. We will examine this formulation in an improved mixed-order finite element and localized radial basis function method. A particle tracking method and the arbitrary Lagrangian-Eulerian scheme will then be applied to simulate the two-dimensional high Reynolds free surface flows. An upwind improved finite element formulation based on a localized radial basis function differential quadrature (LRBFDQ) method is used to deal with high Reynolds number convection dominated flows. This study successfully obtained very high Reynolds number free surface flows, up to Re = 500 000. Finally, we will demonstrate and discuss the capability and feasibility of the proposed model by simulating two complex free surface flow problems: (1) a highly nonlinear free oscillation flow and (2) a large amplitude sloshing problem. Using even very coarse grids in all computing scenarios, we have achieved good results in accuracy and efficiency.

Numerical investigation of scaling effect in two-dimensional oscillating water column wave energy devices for harvesting wave energy

Oscillating water column (OWC) devices utilise wave-induced oscillation of water column in partially submerged chambers to extract energy of waves in ocean. The principal aim of this paper is to investigate scaling effects of two-dimensional OWC through numerical simulations. The fluid motion under waves is simulated by solving the two-dimensional incompressible Reynolds-Averaged Navier-Stokes equations using finite element method under Arbitrary Lagrangian-Eulerian scheme. To investigate scaling effects, the waves and the OWC are scaled up or down according to Froude number similarity. The turbine is scaled up or down using three different scaling methods: (1) Turbine coefficient remains unchanged, i.e. not scaling the turbine at all; (2) Equivalent pneumatic damping coefficient of the turbine is constant and (3) the two-dimensional turbine coefficient is constant. The numerical results show that method (2) has the smallest effects on the best hydraulic efficiency and method (3) has the smallest effects on the best performance wave number, i.e. the wave number where the OWC receives the largest percentage of the wave energy. The worst scaling method is not scaling the turbine. Because the best performance wave number varies with the model scale in method (1) and (2), it is very likely the scaling effects of the model scale on the hydrodynamic performance at different wave numbers are different from each other. In addition, the effects of the wave height and the chamber volume are studied. Increasing chamber volume causes a reduction of the best performance, however it may improve general performance of OWC because it increases the frequency band of waves with high hydraulic efficiency. Increasing wave height causes a reduction of the hydraulic efficiency.

An Arbitrary-Lagrangian-Eulerian High-Order Gas-Kinetic Scheme for Three-Dimensional Computations

In the previous study [J. Comput. Phys. 417 (2020) 109558], under arbitrary-Lagrangian-Eulerian (ALE) formulation a high-order gas-kinetic scheme has been developed for the computation of two-dimensional flows. For the three-dimensional flows, due to the distorted mesh, it becomes more difficult to develop robust high-order ALE methods with the precise preservation of geometric conservation law. In this paper, the high-order gas-kinetic ALE scheme will be constructed for three-dimensional flows. The key ingredients of the scheme are the use of weighted essentially non-oscillatory (WENO) scheme for spatial reconstruction and the two-stage fourth-order discretization for temporal evolution. In the ALE formulation, in order to release the problems associated with mesh distortion and non-coplanar vertexes of a control volume, in the spatial reconstruction the selection of candidate stencils and the topologically independent linear weights have to be carefully designed. In the surface integrals for the flux transport, a bilinear interpolation is used to parameterize both grid coordinates and grid moving velocity with the preservation of the geometric conservation law. In the computation, the grid velocity is determined by the variational formulation based Lagrangian nodal solver. Numerical examples are presented to evaluate the accuracy, robustness, and the preservation of geometric conservation law of the current scheme.

Tear-film breakup: The role of membrane-associated mucin polymers.

Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to elucidate the hydrodynamic mechanisms by which loss of membrane-associated mucins causes premature tear-film rupture. We model the bulk of the tear film as a Newtonian fluid in a two-dimensional periodic domain, and the lipid layer at the air-tear interface as insoluble surfactants. Gradual loss of membrane-associated mucins produces growing areas of exposed cornea in direct contact with the tear fluid. We represent the hydrodynamic consequences of this morphological change through two mechanisms: an increased van der Waals attraction due to loss of wettability on the exposed area, and a change of boundary condition from an effective negative slip on the mucin-covered areas to the no-slip condition on exposed cornea. Finite-element computations, with an arbitrary Lagrangian-Eulerian scheme to handle the moving interface, demonstrate a strong effect of the elevated van der Waals attraction on precipitating tear-film breakup. The change in boundary condition on the cornea has a relatively minor role. Using realistic parameters, our heterogeneous mucin model is able to predict quantitatively the shortening of tear-film breakup time observed in diseased eyes.

High order difference schemes using the local anisotropic basis function method

Mesh-free methods have significant potential for simulations in complex geometries, as the time consuming process of mesh-generation is avoided. Smoothed Particle Hydrodynamics (SPH) is the most widely used mesh-free method, but suffers from a lack of consistency. High order, consistent, and local (using compact computational stencils) mesh-free methods are particularly desirable.Here we present a novel framework for generating local high order difference operators for arbitrary node distributions, referred to as the Local Anisotropic Basis Function Method (LABFM). Weights are constructed from linear sums of anisotropic basis functions (ABFs), chosen to ensure exact reproduction of polynomial fields up to a given order. The ABFs are based on a fundamental Radial Basis Function (RBF), and the choice of fundamental RBF has small effect on accuracy, but influences stability. LABFM is able to generate high order difference operators with compact computational stencils (4th order with N≈25 nodes, 8th order with N≈60 nodes in two dimensions). At domain boundaries (with incomplete support) LABFM automatically provides one-sided differences of the same order as the internal scheme, up to 4th order. We use the method to solve elliptic, parabolic and mixed hyperbolic-parabolic partial differential equations (PDEs), showing up to 8th order convergence. The inclusion of hyperviscosity is straightforward, and can effectively provide stability when solving hyperbolic problems.LABFM is a promising new mesh-free method for the numerical solution of PDEs in complex geometries. The method is highly scalable, and for Eulerian schemes, the computational efficiency is competitive with RBF-FD for a given accuracy. A particularly attractive feature is that in the low order limit, LABFM collapses to Smoothed Particle Hydrodynamics (SPH), and there is potential for Arbitrary Lagrangian-Eulerian schemes with natural adaptivity of resolution and accuracy.

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving two-dimensional Voronoi meshes that are regenerated at each time step and which explicitly allow topology changes in time. The Voronoi tessellations are obtained from a set of generator points that move with the local fluid velocity. We employ an AREPO-type approach [173], which rapidly rebuilds a new high quality mesh exploiting the previous one, but rearranging the element shapes and neighbors in order to guarantee that the mesh evolution is robust even for vortex flows and for very long simulation times. The old and new Voronoi elements associated to the same generator point are connected in space–time to construct closed space–time control volumes, whose bottom and top faces may be polygons with a different number of sides. We also have to incorporate some degenerate space–time sliver elements, which are needed in order to fill the space–time holes that arise because of the topology changes in the mesh between time tn and time tn+1. The final ALE FV-DG scheme is obtained by a novel redesign of the high order accurate fully discrete direct ALE schemes of Boscheri and Dumbser [21,23], which have been extended here to general moving Voronoi meshes and space–time sliver elements. Our new numerical scheme is based on the integration over arbitrary shaped closed space–time control volumes combined with a fully-discrete space–time conservation formulation of the governing hyperbolic PDE system. In this way the discrete solution is conservative and satisfies the geometric conservation law (GCL) by construction. Numerical convergence studies as well as a large set of benchmark problems for hydrodynamics and magnetohydrodynamics (MHD) demonstrate the accuracy and robustness of the proposed method. Our numerical results clearly show that the new combination of very high order schemes with regenerated meshes that allow topology changes in each time step lead to substantial improvements compared to direct ALE methods on moving conforming meshes without topology change.

Forced convection in partially compliant channel with two alternated baffles

This paper investigates the fluid-structure interaction (FSI) and the forced convective heat transfer in a channel partly heated by constant heat flux. The FSI is represented by the 2-dimensional benchmarked geometry; a compliant segment wall. Two alternatives, upstream and downstream, baffles acting as vortex generators bound the compliant segment. The unsteady problem is formulated by arbitrary Lagrangian-Eulerian scheme based on finite element method. The thermal-hydraulic enhancement criterion is computed to evaluate the performance of the channel. Cauchy number and the length of the baffles respectively control the flexibility of the compliant segment and the force exerted on it, while Reynolds number is imposed to assess the competitive roles of the inertia and viscous forces. It is found that the Nusselt number of a certain compliant baffled channel enhances 94% compared with non-baffled channel at Re = 250, while the pressure drop increases by 210%. The thermal-hydraulic analysis shows that the best performance can be obtained at Cauchy number of 10−7 when the lengths of the upstream and downstream baffles are 0.6 and 0.2 times the channel height, respectively. The results show also that the compliant wall segment lowers the thermal performance of the non-baffled channel.

Fluid-structure interaction simulations of venous valves: A monolithic ALE method for large structural displacements.

Venous valves are bicuspidal valves that ensure that blood in veins only flows back to the heart. To prevent retrograde blood flow, the two intraluminal leaflets meet in the center of the vein and occlude the vessel. In fluid-structure interaction (FSI) simulations of venous valves, the large structural displacements may lead to mesh deteriorations and entanglements, causing instabilities of the solver and, consequently, the numerical solution to diverge. In this paper, we propose an arbitrary Lagrangian-Eulerian (ALE) scheme for FSI simulations designed to solve these instabilities. A monolithic formulation for the FSI problem is considered, and due to the complexity of the operators, the exact Jacobian matrix is evaluated using automatic differentiation. The method relies on the introduction of a staggered in time velocity to improve stability, and on fictitious springs to model the contact force of the valve leaflets. Because the large structural displacements may compromise the quality of the fluid mesh as well, a smoother fluid displacement, obtained with the introduction of a scaling factor that measures the distance of a fluid element from the valve leaflet tip, guarantees that there are no mesh entanglements in the fluid domain. To further improve stability, a streamline upwind Petrov-Galerkin (SUPG) method is employed. The proposed ALE scheme is applied to a two-dimensional (2D) model of a venous valve. The presented simulations show that the proposed method deals well with the large structural displacements of the problem, allowing a reconstruction of the valve behavior in both the opening and closing phase.

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well balanced path-conservative finite volume schemes, that are expressly designed to deal with source terms written via nonconservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one and two space dimensions.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination.The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables.In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.

Parallel implementation of a Lagrangian-based model on an adaptive mesh in C++: Application to sea-ice

We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto–Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure Lagrangian scheme or an Arbitrary Lagrangian Eulerian scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.