What are the advancements published on the Semi-Implicit Method for Pressure Linked Equations?
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Advancements in the Semi-Implicit Method for Pressure Linked Equations include the development of a novel pressure-based semi-implicit finite volume solver for compressible ideal, viscous, and resistive magnetohydrodynamics (MHD) equations . Another advancement is the introduction of an accurate semi-implicit rotational projection method for solving the Navier-Stokes equations in incompressible flow simulations . Additionally, a new formulation of the material point method (MPM) has been proposed for modeling coupled soil deformation and pore fluid flow problems, with an implicit treatment of pore-water pressure . Furthermore, a semi-implicit method has been presented for solving the incompressible three-phase flow equations, using a high-order discontinuous Galerkin spatial discretization coupled with a backward Euler discretization in time . These advancements have led to improved accuracy, stability, and efficiency in simulating a wide range of geophysical and engineering problems involving pressure linked equations.
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58 Citations | The paper discusses the extension of semi-implicit methods to complex free-surface flows governed by the full incompressible Navier-Stokes equations. It proposes a numerical algorithm that solves the pressure equation using a nested Newton type iterative scheme. |
| The paper presents a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous, and resistive magnetohydrodynamics (MHD). It describes the discretization of the x-momentum equation and the total energy equation using a semi-implicit method. | |
| The provided paper presents a new formulation of the material point method (MPM) for modeling coupled soil deformation and pore fluid flow problems. It introduces a semi-implicit treatment of pore-water pressure to reduce pressure oscillations and increase the time step size. However, there is no specific mention of advancements published on the semi-implicit method for pressure linked equations in the paper. | |
1 Citations | The paper introduces an accurate semi-implicit rotational projection method for solving the Navier-Stokes equations for incompressible flow simulations. It proposes an alternative way to decouple pressure from the momentum equation and presents discrete forms with arbitrary orders of accuracy. |
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