A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping

Lovrić, Aleksander; Dettmer, Wulf G.; Kadapa, Chennakesava; Perić, D.

doi:10.1016/j.cma.2018.05.006

Cited by 10 publications

(13 citation statements)

References 41 publications

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“…For larger values of , a relative maximum develops. Numerical evidence suggests the same critical value for as given by Equation (47). Hence, very large fluid viscosities may cause stability issues close to the critical amount of added mass.…”

Section: Staggered Schemementioning

confidence: 75%

“…More information on segregated solution schemes for the incompressible Navier-Stokes equations is provided in a recent article 47 by the authors and many references therein. In their article, the authors employ a model problem similar to the one used in the present work to provide insight into such methodologies.…”

Section: Finite Element Method: Projection Schemementioning

confidence: 99%

See 1 more Smart Citation

New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

Dettmer

Lovrić

Kadapa

et al. 2020

Numerical Meth Engineering

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In the presence of strong added mass effects, partitioned solution strategies for incompressible fluid-structure interaction are known to lack robustness and computational efficiency. A number of strategies have been proposed to address this challenge. However, these strategies are often complicated or restricted to certain problem classes and generally require intrusive modifications of existing software. In this work, the well-known Dirichlet-Neumann coupling is revisited and a new combined two-field relaxation strategy is proposed. A family of efficient staggered schemes based crucially on a force predictor is formulated alongside the classical iterative approach. Both methodologies are rigorously analyzed on the basis of a linear model problem derived from a simplified fluid-conveying elastic tube. The investigation suggests that both the robustness and the efficiency of a partitioned Dirichlet-Neumann coupling scheme can be improved by a relatively small nonintrusive modification of a standard implementation. The relevance of the model problem analysis for finite element-based computational fluid-structure interaction is demonstrated in detail for a submerged cylinder subject to an external force.

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Section: Staggered Schemementioning

confidence: 75%

Section: Finite Element Method: Projection Schemementioning

confidence: 99%

New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

Dettmer

Lovrić

Kadapa

et al. 2020

Numerical Meth Engineering

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“…For ρ ∞ = 0, the scheme annihilates all the high-frequency modes after the first time step. The GA scheme is spectrally equivalent to the second-order accurate backward-difference formula (BDF2), for ρ ∞ = 0, see [22] for details. Thus, by choosing ρ ∞ appropriately, different time integration schemes can be recovered from the GA scheme.…”

Section: Bdf Schemesmentioning

confidence: 99%

“…Iterative solution techniques in the fractional-step and projection schemes are avoided by choosing v h φ 3 = v h n , which, unfortunately, limits the order of temporal accuracy to one, even with higher-order accurate time integration schemes for the viscous and pressure gradient terms. Second-order temporal accuracy can be achieved by choosing appropriate extrapolation for the convective velocity field, see [22] for the details.…”

Section: Formulation With Linearised Convection Operatorsmentioning

confidence: 99%

Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction

Kadapa

Dettmer

Perić

2020

Journal of Fluids and Structures

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Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton-Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf-sup stable P2-P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid-structure interaction problems is illustrated using two benchmark examples in fluid-flexible structure interaction.

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“…For example, in [6], a hybrid model reduction scheme to approximate the Navier-Stokes equations (NSE) with a low-dimensional model on a contraction geometry is presented. The use of a novel projection method based on midpoint rule for the solution of NSE is discussed in [13]. In [8], Guermond and Minev develop a high-order time approximation for the NSE as an alternative for the classical projection method.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Newtonian Flows on Sudden Contraction Geometries: GPU Implementation

Alvarado¹,

Tapia²,

Ceniceros³

2018

RCS

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In this paper, a GPU-based simulation of a Newtonian fluid flow on sudden contraction geometries is presented. The fluid is modeled with the Navier-Stokes equations and solved by the projection method with first order in time and second order in space discretizations. A semi-implicit scheme of finite differences is used in the dicretization process. The solution of the resulting system of linear equations is considered as an optimization problem and is solved by the preconditioned biconjugate gradient stabilized method (BiCGSTAB) implemented on a graphic processor using the CUDA libraries cuSPARSE and cuBLAS.

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A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping

Abstract: A new family of projection schemes for the incompressible Navier-Stokes equations with control of high-frequency damping.

Cited by 10 publications

References 41 publications

New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction

Simulation of Newtonian Flows on Sudden Contraction Geometries: GPU Implementation

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