An overview of projection methods for incompressible flows
By Jean-Luc Guermond, Peter Dimitrov Minev, Jie Shen. 2006
1,512 citations recorded by the source corpus.
Subfields: Computational Mechanics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/379ebc81b43a7e103f4e2edba441d18f97ee8519
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In Computational Mechanics
In Numerical Analysis
Citations in the corpus
- Development of a fast fluid dynamics-based adjoint method for the inverse design of indoor environments (2017, methodology): “…this study also investigated three pressure-correction schemes without the SL scheme: the non-incremental pressure-correction (NIPC) scheme, standard incremental pressure-correction (SIPC) scheme, and rotational incremental pressure-correction (RIPC) scheme (Guermond, Minev, and Shen 2006).”
- Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “This “splitting error” associated with the fractional step method is known to be first or second order in time depending on whether the pressure is explicitly included or not included at all in the first velocity step (Guermond et al., 2006).”
- Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows (2010, methodology): “[20, 22, 8 , 10]) which only require solving a pressure Poisson equation.”
- Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization (2013, methodology): “Solving Oseen-type systems has a long history and there are dozens of different solution approaches ranging from Uzawa type methods [2] to projection methods [3], special multi-grid methods [4] or block saddle point preconditioners [5, 6, 7].”
- A new class of massively parallel direction splitting for the incompressible Navier―Stokes equations (2011, methodology): “Most of the time marching algorithms that are used in Computation Fluid Mechanics to solve large scale incompressible fluids flows are based on the so-called projection methods (see Chorin [5] and Temam [24] for the earliest examples and [12] for a recent review).”
- Least squares moving particle semi-implicit method (2014, methodology): “this non-physical inconsistent Neumann boundary conditions enforced on the pressure introduces the numerical boundary layer which limits the accuracy of time integration schemes [33,83].”
- A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid (2007, background): “Moreover, its stability properties, observed in various complex numerical simulations, are confirmed by a theoretical analysis carried out in a simplified configuration.”
- Stability and convergence of efficient Navier‐Stokes solvers via a commutator estimate (2007, methodology): “A similar observation is made in [20] for the linear case with smooth solutions and homogeneous boundary conditions.”
- Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows (2015, neutral): “the review [12] and the references therein).”
- A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities (2010, methodology): “…observation led Guermond and Salgado [8] to construct a scheme for the Navier–Stokes equations with variable density, based on pressure stabilization (cf., for instance, [20] [25] [18] [9]), namely, the divergence-free condition is replaced by (3.25) ∇ · u − δΔp t = 0, where δ is a small parameter.”
- A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals (2017, methodology): “the references in the overview of projection method in [15]).”