Space-time discretizing optimal DRP schemes for flow and wave propagation problems

Sengupta, Tapan K.; Rajpoot, Manoj K.; Bhumkar, Yogesh G.

doi:10.1016/j.compfluid.2011.03.003

Cited by 51 publications

(11 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This will lead to higher mismatch with the POD data, due to higher sensitivity of phase match from the solution of Eqs. (34) to (37) for any off-center point.…”

Section: Reconstruction Of Disturbance Vorticity From the Sle Smentioning

confidence: 99%

See 1 more Smart Citation

Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow past a cylinder

et al. 2015

View full text Add to dashboard Cite

Here proper orthogonal decomposition (POD) modal decomposition are performed for flow past a circular cylinder at supercritical Reynolds numbers by projecting this onto instability modes. The important task of modeling a cylinder wake by Stuart-Landau (SL) and the Stuart-Landau-Eckhaus (SLE) equation for instability modes is discussed, with the latter shown to be more consistent with multimodal pictures of POD and instability modes. The difficult task of finding the coefficients of the SLE equation is reported by taking a least squares approach for the reduced order model (ROM). The important aspect of the ROM is the choice of initial condition for the developed SLE equations, as these are stiff ordinary differential equations which are very sensitive to the choice of initial conditions. An accurate representation of enstrophy-based POD also reveals the presence of modes which occur in isolation (in comparison to modes that come in pairs) and the traditional approach of treating instability modes by SL or SLE equations does not work directly, which also reveals higher frequency variations. Quantifying effects of this mode by time-averaged Navier-Stokes equation (NSE) fail to show the variation of the phase of these isolated time-varying modes and this is captured here using direct numerical simulation (DNS) data by a multitime scale approach. A reconstructed 3-mode ROM solution and the disturbance vorticity from DNS match globally in the flow. The agreement between 3-mode SLE reconstruction and DNS also proves the consistency of the proposed method and helps explain the physical nature of the ensuing Hopf bifurcation following an instability.

show abstract

“…This will lead to higher mismatch with the POD data, due to higher sensitivity of phase match from the solution of Eqs. (34) to (37) for any off-center point.…”

Section: Reconstruction Of Disturbance Vorticity From the Sle Smentioning

confidence: 99%

“…A central differencing scheme is used to discretize the Laplacian operator of Eqs. (8) and (9) and an optimized four-stage, third-order Runge-Kutta (OCRK3) method designed in [34] is employed for time marching. Equation (8) is solved using the Bi-CGSTAB method of Van der Vorst [35].…”

Section: -3mentioning

confidence: 99%

Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow past a cylinder

et al. 2015

View full text Add to dashboard Cite

show abstract

“…(23). An optimized dispersion relation preserving (DRP) Runge-Kutta scheme OCRK3, developed in Sengupta et al 53 , has been used for time integration. The diffusion terms of Eq.…”

Section: Governing Fluid Dynamic Equationsmentioning

confidence: 99%

New Frequency Dependent Capacitance Based SDBD Plasma Model for Direct Simulation of 2D Navier-Stokes Equation

Sengupta

Bagade

2016

47th AIAA Plasmadynamics and Lasers Conference

Self Cite

View full text Add to dashboard Cite

The effects of single dielectric barrier discharge (SDBD) plasma actuators on flow control are studied using a new frequency and pressure dependent capacitance based model by calculating the spatio-temporal distribution of surface charge density in the present work. The proposed model is an improvement over earlier similar efforts, while retaining the superior features of previous macroscopic models. It can be used to accurately compute the spatio-temporal distribution of body force due to plasma actuation without computing the complex electrodynamics equations for charge density on microscopic scales. It has been shown that the proposed model estimates the time-averaged total body force more accurately than similar models developed earlier, as compared to experimental results. We have also considered the effects of plasma excitation frequency and the voltage wave-form. The proposed model has been incorporated into a Navier-Stokes equation (NSE) solver in time-accurate manner to study SDBD plasma actuation in a quiescent flow environment. The onset of plasma actuation causes creation of a complex transient vortical flow field, one of its actions is to create a wall-jet. Computed instantaneous velocity profiles at downstream locations show this wall-jet and are compared with the experimental results. Computed results of the evolution of a starting vortex in a quiescent air induced by initiation of SDBD plasma actuation, displays an excellent match with experimental results of Whalley and Choi (J. Fluid Mech., 703, 192-203, 2012).

show abstract

“…VTE is time advanced using OCRK3 technique [40], which has superior dispersion relation preservation properties.…”

Section: Time Integration Schemementioning

confidence: 99%

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

Bagade¹,

Krishnan²,

Sengupta³

2015

FAE

View full text Add to dashboard Cite

Here, Direct Numerical Simulation (DNS) of low Reynolds number (Re) flow in the presence of free stream turbulence (FST) pertaining to micro-aerial vehicle (MAV) is reported. The focus is on numerically simulating the flow around an airfoil at low Re to understand its behaviour using high accuracy compact schemes (T. K. Sengupta, High Accuracy Computing Methods, Cambridge University Press, New York, 2013.) [1]. In low Re aerodynamics, the flow is characterized by unsteady separation bubbles and vortex shedding from the suction surface and the trailing edge as well, which make it different from high Re aerodynamics. The maximum attainable lift coefficient and lift-to-drag ratio decreases drastically at low Re, as compared to high Re flows. Such flows are also important because of their susceptibility to background disturbances. Stalling of aircraft wing is one such phenomenon where free stream turbulence (FST) plays a crucial role. In this work, effects of FST, effects of Re and angles of attack  are studied with respect to flow separation and vortex shedding. Flow characterization is done for the AG24 airfoil, at Re =60,000 and 400,000, with and without consideration of FST in the range of angles of attack, 6 6The computational results are compared with the experimental results of Williamson et al. ( Summary of Low Speed Airfoil Data, volume 5, Dept. of Aerospace Engineering, UIUC, 2007 ) [2] and are found to be in good agreement. Flow simulation over AG24 airfoil is performed here via parallel computation, using high accuracy compact schemes for spatial discretization and optimized Runge-Kutta (ORK4) scheme for time marching [1]. This paper also discusses proper implementation of filters and FST model.

show abstract

Space-time discretizing optimal DRP schemes for flow and wave propagation problems

Cited by 51 publications

References 26 publications

Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow past a cylinder

Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow past a cylinder

New Frequency Dependent Capacitance Based SDBD Plasma Model for Direct Simulation of 2D Navier-Stokes Equation

DNS of Low Reynolds Number Aerodynamics in the Presence of Free Stream Turbulence

Contact Info

Product

Resources

About