Acceleration of Later Convergence in a Density-Based Solver Using Adaptive Time Stepping

Kalkote, Nikhil Narayan; Assam, Ashwani; Eswaran, V.

doi:10.2514/1.j057014

Cited by 12 publications

(10 citation statements)

References 36 publications

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“…We have implemented the non-equilibrium boundary condition in our in-house 3D unstructured grid solver which has been thoroughly validated for various configurations of flows (Sharma et al , 2016; Kalkote et al , 2018a; 2018b, Assam et al , 2018a ). The first order Maxwell Slip [equation (11)] and Smoluchowski temperature jump [equation (12)] boundary condition has been implemented in the solver and verified for various configuration of the micro/nano flows (Assam et al , 2017).…”

Section: Resultsmentioning

confidence: 99%

Investigation of non-equilibrium boundary conditions considering sliding friction for micro/nano flows

Assam

Kalkote

Dongari

et al. 2019

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Purpose Accurate prediction of temperature and heat is crucial for the design of various nano/micro devices in engineering. Recently, investigation has been carried out for calculating the heat flux of gas flow using the concept of sliding friction because of the slip velocity at the surface. The purpose of this study is to exetend the concept of sliding friction for various types of nano/micro flows. Design/methodology/approach A new type of Smoluchowski temperature jump considering the viscous heat generation (sliding friction) has recently been proposed (Le and Vu, 2016b) as an alternative jump condition for the prediction of the surface gas temperature at solid interfaces for high-speed non-equilibrium gas flows. This paper investigated the proposed jump condition for the nano/microflows which has not been done earlier using four cases: 90° bend microchannel pressure-driven flow, nanochannel backward facing step with a pressure-driven flow, nanoscale flat plate and NACA 0012 micro-airfoil. The results are compared with the available direct simulation Monte Carlo results. Also, this paper has demonstrated low-speed preconditioned density-based algorithm for the rarefied gas flows. The algorithm captured even very low Mach numbers of 2.12 × 10−5. Findings Based on this study, this paper concludes that the effect of inclusion of sliding friction in improving the thermodynamic prediction is case-dependent. It is shown that its performance depends not only on the slip velocity at the surface but also on the mean free path of the gas molecule and the shear stress at the surface. A pressure jump condition was used along with the new temperature jump condition and it has been found to often improve the prediction of surface flow properties significantly. Originality/value This paper extends the concept of using sliding friction at the wall for micro/nano flows. The pressure jump condition was used which has been generally ignored by researchers and has been found to often improve the prediction of surface flow properties. Different flow properties have been studied at the wall apart from only temperature and heat flux, which was not done earlier.

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Section: Resultsmentioning

confidence: 99%

Investigation of non-equilibrium boundary conditions considering sliding friction for micro/nano flows

Assam

Kalkote

Dongari

et al. 2019

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“…To reduce the size of the nonlinear system for implicit stages ( a ii ≠ 0 ), we choose to rewrite the discrete counterparts of Eqs. (11)- (12) as since the length of is usually smaller than that of . In rewriting the above equations, the relations of Eqs.…”

Section: Discrete Formulationmentioning

confidence: 99%

“…Bücker et al compared some of the existing adaptive methods in 2009 and concluded that there is no clear winner [6]. In 2019, an error based adaptive CFL method was developed to accelerate the late stage of convergence but still need to manually divide the convergence history into different stages [12]. Compared with the studies on efficiency, much fewer studies have focused on robustness.…”

Section: Introductionmentioning

confidence: 99%

Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

Pan

Yan

Peiró

et al. 2021

Commun. Appl. Math. Comput.

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A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded Runge-Kutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously influencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state flow past a flat plate, Taylor-Green vortex and turbulent flow over a circular cylinder at $${Re}=3\,900$$ Re = 3 900 . The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efficiency is obtained for unsteady and steady, well-resolved and under-resolved simulations.

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“…The gradients are computed with the Green-Gauss method and Venkatakrishnan's limiter (Assam and Eswaran, 2019) is used to avoid spurious oscillations in the presence of sharp discontinuities, if there are any. The in-house solver has been extensively validated for single-species flows Assam and Eswaran, 2019;Kalkote et al, 2018), both laminar and turbulent, that need not again be tested here. Therefore, this section demonstrates the stability and verification only of the 0 Chemically reacting flows implemented numerical framework for handling the strong source terms and the correct computations of the chemical reactions.…”

Section: Verification Of the Implementationmentioning

confidence: 99%

Toward the implementation of a multi-component framework in a density-based flow solver for handling chemically reacting flows

Kalkote

Assam

Eswaran

2020

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Purpose The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which rely on chemical reactions as their operational mechanism, with heat generated from the combustion of the fuel, often gases, being converted to work. Design/methodology/approach The numerical study of such flows requires the set of Navier-Stokes equations to be extended to include multiple species and the chemical reactions between them. The numerical method implemented in this study also accounts for changes in the material properties because of temperature variations and the process to handle steep spatial fronts and stiff source terms without incurring any numerical instabilities. An all-speed numerical framework is used through simple low-dissipation advection upwind splitting (SLAU) convective scheme, and it has been extended in a multi-component species framework on the in-house density-based flow solver. The capability of solving turbulent combustion is also implemented using the Eddy Dissipation Concept (EDC) framework and the recent k-kl turbulence model. Findings The numerical implementation has been demonstrated for several stiff problems in laminar and turbulent combustion. The laminar combustion results are compared from the corresponding results from the Cantera library, and the turbulent combustion computations are found to be consistent with the experimental results. Originality/value This paper has extended the single gas density-based framework to handle multi-component gaseous mixtures. This paper has demonstrated the capability of the numerical framework for solving non-reacting/reacting laminar and turbulent flow problems. The all-speed SLAU convective scheme has been extended in the multi-component species framework, and the turbulent model k-kl is used for turbulent combustion, which has not been done previously. While the former method provides the capability of solving for low-speed flows using the density-based method, the later is a length-scale-based method that includes scale-adaptive simulation characteristics in the turbulence modeling. The SLAU scheme has proven to work well for unsteady flows while the k-kL model works well in non-stationary turbulent flows. As both these flow features are commonly found in industrially important reacting flows, the convection scheme and the turbulence model together will enhance the numerical predictions of such flows.

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Acceleration of Later Convergence in a Density-Based Solver Using Adaptive Time Stepping

Cited by 12 publications

References 36 publications

Investigation of non-equilibrium boundary conditions considering sliding friction for micro/nano flows

Investigation of non-equilibrium boundary conditions considering sliding friction for micro/nano flows

Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

Toward the implementation of a multi-component framework in a density-based flow solver for handling chemically reacting flows

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