Energy preserving turbulent simulations at a reduced computational cost

Capuano, Francesco; Coppola, Gennaro; Balarac, Guillaume; Luca, Luigi De

doi:10.1016/j.jcp.2015.06.011

Cited by 23 publications

(31 citation statements)

References 35 publications

(62 reference statements)

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“…When dealing with implicit (central) compact schemes, however, it is not clear if the discretization of the nonlinear convective term in Equation (35) can be performed directly on the divergence form and still retaining the global conservation of kinetic energy at the discrete level. In this case, the employment of the so-called skew-symmetric splitting is mandatory, as in the case of regular layouts, since it automatically guarantees conservation of global kinetic energy on a semi-discrete level [29].…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…In this case, the employment of the so-called skew-symmetric splitting is mandatory, as in the case of regular layouts, since it automatically guarantees conservation of global kinetic energy on a semi-discrete level [29]. Recently, other approaches have been proposed, in which the beneficial properties of the skew-symmetric splitting are obtained by properly alternating the more economic divergence and advective forms inside the stages of a multistage time integration procedure [34][35][36]. In this paper, we will not consider these more sophisticated techniques, and will instead rely on the classical skew-symmetric form for the convective term.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…One-dimensional derivatives of zeroth, first, and second order are used to discretize spatial operators involved in the computation of the non-linear convective as well as linear viscous terms in Equation (35). While the latter does not require any special attention, the former does, due to its non linearity.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…The perturbation on the v-velocity is used to promote the roll-up of the shear layer; as in [35], = 0.05 is used. A single instability mode is activated by choosing δ = π/15.…”

Section: Periodic Double Mixing Layermentioning

confidence: 99%

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Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Angelis¹,

Coppola²,

Capuano³

et al. 2018

Applied Sciences

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A method is proposed for the derivation of new classes of staggered compact derivative and interpolation operators. The algorithm has its roots in an implicit interpolation theory consistent with compact schemes and reduces to the computation of the required staggered derivatives and interpolated quantities as a combination of nodal values and collocated compact derivatives. The new approach is cost-effective, simplifies the imposition of boundary conditions, and has improved spectral resolution properties, on equal order of accuracy, with respect to classical schemes. The method is applied to incompressible Navier-Stokes equations through the implementation into a staggered flow solver with a fractional step procedure, and tested on classical benchmarks.

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Section: Spatial Discretizationmentioning

confidence: 99%

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Spatial Discretizationmentioning

confidence: 99%

“…The perturbation on the v-velocity is used to promote the roll-up of the shear layer; as in [35], = 0.05 is used. A single instability mode is activated by choosing δ = π/15.…”

Section: Periodic Double Mixing Layermentioning

confidence: 99%

See 2 more Smart Citations

Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Angelis¹,

Coppola²,

Capuano³

et al. 2018

Applied Sciences

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“…which is defined as a suitable average of the divergence and advective formulations, whose errors on energy conservation are equal and of opposite sign [2]. This choice, however, has the drawback of being roughly twice as expensive as standard divergence or advective forms alone.…”

Section: Introductionmentioning

confidence: 99%

Low-Cost Energy-Preserving RK Schemes for Turbulent Simulations

Capuano

Coppola

Luca

2016

Springer Proceedings in Physics

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A low-cost numerical strategy is presented for energy-preserving simulations of incompressible flows. This method consists in an explicit Runge-Kutta scheme in which the divergence and advective forms of the convective term are suitably alternated within the sub-steps. As a result, the conservation properties of the skew-symmetric form are recovered at a reduced computational cost. The performances and the accuracy of the method are proved by numerical simulations.

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Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

Edoh

Mundis

Karagozian

et al. 2020

Numerical Methods in Fluids

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The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.

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Energy preserving turbulent simulations at a reduced computational cost

Cited by 23 publications

References 35 publications

Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Low-Cost Energy-Preserving RK Schemes for Turbulent Simulations

Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

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