Accurate projection methods for the incompressible Navier—Stokes equations

By David L. Brown, R. Cortez, Michael L. Minion. 2001

927 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/978a511ca30a6c5af90456800efb5548ddad4e6f

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Citations in the corpus

USING THE PARTICLE LEVEL SET METHOD AND A SECOND ORDER ACCURATE PRESSURE BOUNDARY CONDITION FOR FREE SURFACE FLOWS (2003, methodology): “A pressure free projection method [6, 7 ] is used to calculate a divergence free velocity field during an Euler time step”
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains (2003, methodology): “based on the primitive variables formulation for problems with small to medium-sized Reynolds numbers, such as the projection method, see [3, 5, 26].”
Conservative multigrid methods for Cahn-Hilliard fluids (2004, neutral): “Thepressureis thenupdatedusingthesecond-order accuratescheme[12]: ;A 1⁄2 » 1⁄4 Û dx1⁄2 O ÆlA 1⁄2 » 1⁄4 Û d H L P( L â, b (42) We notethatcombiningEqs.”
Analysis of an Exact Fractional Step Method (2002, background): “The price is a certain loss of temporal accuracy in the solution, which is the subject of many articles [1–3] and some debate about how boundary conditions should be specified [4–6], which may now be largely resolved [7, 8], and some difficulties if convection is treated implicitly [9].”
SPH with the multiple boundary tangent method (2009, neutral): “[21].”
Numerical methods for incompressible viscous flow (2002, methodology): “A typical fractional step approach [2, 4, 10, 20, 87] may start with a time discretization where the convective term is treated explicitly, whereas the pressure and the viscosity term are treated implicitly: v − v + ∆tv · ∇v = −∆t ̺ ∇p + ∆tν∇(2)v + ∆tg, (73) ∇ · v = 0 .”
A second-order method for three-dimensional particle simulation (2005, methodology): “For each iteration, the first step is executed by the second-order-accurate projection method described in [55] suitably modified for the present purposes as we now explain.”
Stability and convergence of efficient Navier‐Stokes solvers via a commutator estimate (2007, background): “[8] for a study of secondorder accuracy near the boundary for several modern improvements of the projection method.”
Drop impact on a solid surface: short-time self-similarity (2015, positive): “Note that the occurrence of sporadic glitches in the numerical solution (see e.g. figures 17 and 25 or 26) are to be related with the classic difficulty of computing the pressure in projection methods, such as the one implemented in Gerris (Brown, Cortez & Minion 2001; Popinet 2003).”
An overview of projection methods for incompressible flows (2006, methodology): “In [6], Brown, Cortez and Minion showed, using a normal modes analysis in a semi-infinite periodic channel, that the pressure approximation in the rotational formulation of the incremental pressure-correction algorithm is second-order accurate.”
A new class of truly consistent splitting schemes for incompressible flows (2003, background): “This class of schemes are now widely used in practice and have been rigorously analyzed in [4,6,11,22,23].”
An Immersed Interface Method for Incompressible Navier-Stokes Equations (2003, methodology): “This quantity is called φ in [2] and they note, following Kim and Moin [9], that for “pressure-free projection methods” a more accurate approximation to the pressure is obtained as”
A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change (2007, methodology): “We adopt a standard projection method [6] (see also [4,14]) for solving the incompressible Navier–Stokes equations and an implicit Crank–Nicholson scheme for solving the heat equation.”
The immersed interface method for the Navier-Stokes equations with singular forces (2001, methodology): “The projection method that we used in this paper is the one described in [2] which is based on the pressure increment formulation of [1, 15] with an additional accurate pressure correction (in [2]; the method is denoted by Pm II).”