Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

Xiu, Dongbin; Sherwin, Spencer J.; Dong, Shen; Karniadakis, George Em

doi:10.1007/bf02728994

Cited by 7 publications

(9 citation statements)

References 32 publications

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“…An intriguing finding is that the error of RLFPM decreases as the time step increases in a certain range. Nevertheless, the same feature has been already discovered in a similar mesh-based method, semi-Lagrangian method [65]. Falcone and Ferretti [66] showed that the overall error of semi-Lagrangian method is indeed not monotonic with respect to time step ∆t and it has the particular form:…”

Section: Taylor-green Flowmentioning

confidence: 53%

A regularized Lagrangian finite point method for the simulation of incompressible viscous flows

Fang

Parriaux

2008

Journal of Computational Physics

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In this paper we present a regularized Lagrangian finite point method (RLFPM) for the numerical simulation of incompressible viscous flows. A Lagrangian finite point scheme is applied to the projection method for the incompressible Navier-Stokes equations. The approximation of spatial derivatives is obtained by the weighted least squares method. The pressure Poisson equation with Neumann boundary condition is solved by a stabilized finite point method. A key aspect of the present approach is the periodic redistribution of the particle locations, which are being distorted by the flow. Again, weighted least squares approximation is implemented to interpolate the properties of the old particles onto the new particle locations. With the proposed regularization technique, problems associated with the flow-induced irregularity of particle distribution in the Lagrangian finite point scheme are circumvented. Three numerical examples, Taylor-Green flow, lid-driven flow in a cavity and flow through a periodic lattice of cylinders, are presented to validate the proposed methodology. The problem of extra diffusion caused by regularization is discussed. The results demonstrate that RLFPM is able to perform accurate and stable simulations of incompressible viscous flows.

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Section: Taylor-green Flowmentioning

confidence: 53%

A regularized Lagrangian finite point method for the simulation of incompressible viscous flows

Fang

Parriaux

2008

Journal of Computational Physics

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“…This requires the solution at the foot of the characteristic (departure point) from each discrete mesh point. This can be done either by a backward particle tracking or by solving an auxiliary advection equation, respectively referred to as the strong form and the auxiliary form of the semi-Lagrangian method in [37].…”

Section: Discussionmentioning

confidence: 99%

An unconditionally stable rotational velocity-correction scheme for incompressible flows

Dong

Shen

2010

Journal of Computational Physics

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We present an unconditionally stable splitting scheme for incompressible Navier-Stokes equations based on the rotational velocity-correction formulation. The main advantages of the scheme are: (i) it allows the use of time step sizes considerably larger than the widely-used semi-implicit type schemes: the time step size is only constrained by accuracy; (ii) it does not require the velocity and pressure approximation spaces to satisfy the usual inf-sup condition: in particular, the equal-order finite element/spectral element approximation spaces can be used; (iii) it only requires solving a pressure Poisson equation and a linear convection-diffusion equation at each time step. Numerical tests indicate that the computational cost of the new scheme for each time step, under identical time step sizes, is even less expensive than the semi-implicit scheme with low element orders. Therefore, the total computational cost of the new scheme can be significantly less than the usual semi-implicit scheme.

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“…To overcome this restriction, we implement a semi-Lagrangian subcycling method for the INS equations which can be viewed as a high-order operator integration factor splitting approach of Maday et.al. (Maday et al, 1990), and is similar to the semi-Lagrangian subcycling approach presented in (Xiu et al, 2005). The splitting scheme (17a)-(17d) provides a natural setting for the subcycling method by separating the advection step from the elliptic parts.…”

Section: A Lagrangian Subcycling Methodsmentioning

confidence: 99%

“…To further improve the performance of the semi-implicit splitting, we also adopt a semi-Lagrangian subcycling approach, which is closely related to the operator integration factor splitting (OFIS) method (Maday et al, 1990). Stability, dispersion, and dissipation properties of the subcycling approaches are discussed in (Giraldo, 2003;Xiu et al, 2005).…”

mentioning

confidence: 99%

A GPU accelerated discontinuous Galerkin incompressible flow solver

Karakus

Chalmers

Świrydowicz

et al. 2019

Journal of Computational Physics

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Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

Cited by 7 publications

References 32 publications

A regularized Lagrangian finite point method for the simulation of incompressible viscous flows

A regularized Lagrangian finite point method for the simulation of incompressible viscous flows

An unconditionally stable rotational velocity-correction scheme for incompressible flows

A GPU accelerated discontinuous Galerkin incompressible flow solver

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