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An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

Communications on Applied Mathematics and Computation 2024年第3期6卷 1665-1719页

作者： Walter Boscheri Raphael Loubere Pierre-Henri Maire Dipartimento di Matematica e Informatica University of FerraraFerraraItaly Institut de Mathématiques de Bordeaux(IMB) University of BordeauxTalenceFrance CEA-CESTA Le BarpFrance

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial *** cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity *** construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under *** is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV *** momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a *** observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler *** this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola ***,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic ***,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each *** conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given *** balance corresponds to a vectorial system satisfied by the nodal *** always admits a unique solution which provides the nodal velocit

关键词： Cell-centered Lagrangian finite-volume(FV)schemes hyper-elasticity Ideal magnetohydrodynamics(MHD)equations Moving unstructured meshes A posteriori MOOD limiting

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An explicit integration scheme for hypo-elastic viscoplastic crystal plasticity

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Transactions of Nonferrous Metals Society of China 2014年第7期24卷 2401-2407页

作者： K.ZHANG B.HOLMEDAL S.DUMOULIN O.S.HOPPERSTAD Department of Materials Science and Engineering Norwegian University of Science and Technology SINTEF Materials and Chemistry Department of Structural Engineering Norwegian University of Science and Technology Structural Impact Laboratory (SIMLab) Center for Research-based InnovationNorwegian University of Science and Technology

An explicit integration scheme for rate-dependent crystal plasticity （CP） was developed. Additive decomposition of the velocity gradient tensor into lattice and plastic parts is adopted for describing the kinematics; the Cauchy stress is calculated by using a hypo-elastic formulation, applying the Jaumann stress rate. This CP scheme has been implemented into a commercial finite element code （CPFEM）. Uniaxial compression and roiling processes were simulated. The results show good accuracy and reliability of the integration scheme. The results were compared with simulations using one hyper-elastic CPFEM implementation which involves multiplicative decomposition of the deformation gradient tensor. It is found that the hypo-elastic implementation is only slightly faster and has a similar accuracy as the hyper-elastic formulation.

关键词： crystal plasticity hypo-elasticity hyper-elasticity forward Euler integration

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