104 research outputs found
A variational formulation for constitutive laws described by bipotentials
Inspired by the algorithm of Berga and de Saxce for solving the
discretisation in time of the evolution problem for an implicit standard
material, we propose a general variational formulation in terms of
bipotentials
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A review on approaches to solving Poissonâs equation in projection-based meshless methods for modelling strongly nonlinear water waves
Three meshless methods, including incompressible smooth particle hydrodynamic (ISPH), moving particle semi-implicit (MPS) and meshless local PetrovâGalerkin method based on Rankine source solution (MLPG_R) methods, are often employed to model nonlinear or violent water waves and their interaction with marine structures. They are all based on the projection procedure, in which solving Poissonâs equation about pressure at each time step is a major task. There are three different approaches to solving Poissonâs equation, i.e. (1) discretizing Laplacian directly by approximating the second-order derivatives, (2) transferring Poissonâs equation into a weak form containing only gradient of pressure and (3) transferring Poissonâs equation into a weak form that does not contain any derivatives of functions to be solved. The first approach is often adopted in ISPH and MPS, while the third one is implemented by the MLPG_R method. This paper attempts to review the most popular, though not all, approaches available in literature for solving the equation
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