Yogesh G. Bhumkar

Spurious waves in discrete computation of wave phenomena and flow problems

In the present work, we focus on spurious propagating disturbances (q-waves). To establish the existence of q-waves in computations, we compare properties of different numerical methods drawn from finite difference, finite volume and finite element methods. Existence and properties of q-waves are demonstrated with propagation of wave-packets following one-dimensional (1D) convection equation; skewed wave propagation and by solution of linearized rotating shallow water wave equation (LRSWE). Specific numerical experiments are performed with parameters that convert a wave-packet into a q-wave. We also show the case where q-waves are created additionally to physical disturbances those propagate downstream. Formation of q-waves are shown in the case of a discrete shielded vortex in the uniform flow and incompressible transitional flow past an aerofoil by solving the Navier–Stokes equation. In performing this exercise, we establish critical wavenumber range beyond which q-waves are created. Relevance of this information for DNS and LES is discussed. We have further discussed the case of spurious caustics in discrete computing.

A dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations

In this work, we have derived an optimized upwind compact difference scheme for achieving excellent spatial resolution. The derived numerical scheme adds numerical diffusion which is strictly restricted to a high wavenumber region in order to control numerical instabilities, as well as to achieve de-aliasing ability. More importantly, the derived numerical scheme has excellent dispersion relation preserving (DRP) property. The applicability of the proposed scheme in simulating real flow problems has been demonstrated by solving flow inside a lid driven cavity, a transitional flow past AG24 aerofoil and a two-dimensional decaying turbulence flow.

Dispersion Relation Preserving Combined Compact Difference Schemes for Flow Problems

In this work, we have proposed two new combined compact difference (CCD) schemes for the solution of Navier–Stokes equations. These spatial discretization schemes have not only high spectral resolution for obtaining first and second derivative terms, but also have improved dispersion relation preserving properties when the fourth-order four-stage Runge–Kutta scheme is used for time integration. Out of the two proposed CCD schemes, the first scheme has upwind stencil, while the second scheme has a central stencil. Important numerical properties of these schemes have been analyzed and their effectiveness have been shown by solving the model wave equations, as well as Navier–Stokes equations. Results show that the upwind CCD scheme is suitable for high accuracy large eddy simulation of transitional and turbulent flowfields.

Drag reduction by rotary oscillation for flow past a circular cylinder

With the help of computational results of incompressible flow past a circular cylinder at Reynolds numbers of Re = 150 and 1000, we explain two possible mechanisms for the experimentally observed drag reduction by rotary oscillation. Here, detailed computed results are compared with available experimental and computational results in Thiria et al. (J Fluid Mech 2006; 560:123-147) for Re = 150. The time-varying loads and moments for various cases have been analyzed first to study bluff body flow control at low Reynolds numbers. We specifically focus upon the effects of amplitude and frequency of the rotary oscillation. Furthermore, to study the effects of Reynolds number, we report another case for a higher Reynolds number of Re = 1000. Proper orthogonal decomposition of computational data for these two Re cases have been performed to explain physical mechanisms behind drag reduction by rotary oscillation and reduced order modeling for different parameter combinations. We show that the drag reduction at th...

A linear focusing mechanism for dispersive and non-dispersive wave problems

A linear focusing mechanism for a wave-packet propagation in a non-periodic domain is explained here using Fourier-Laplace spectral theory. The global analysis method is used here to obtain numerical properties at each node of the full domain. In this work, we show the spectacular growth of an error-packet at a particular node and wavenumber, a phenomenon termed as focusing which depends on: (a) CFL number, N c and (b) numerical method used for discretization. In this study, we have shown the focusing phenomenon for the numerical solution of the 1D convection equation and linearized rotating shallow water equation.

Control of Bypass Transitional Flow Past an Aerofoil by Plasma Actuation

In this work, we have studied effects of plasma actuation while controlling bypass transition of flow over the top surface of DU96-W-180 aerofoil. We have discussed some of the important plasma simulation models proposed in the literature and presented results using a hybrid model given by [Lemire and Vo, J. Turbomach., 2011, 133(1), 011017]. Results show that the computed body force is localized near the electrodes. Due to action of plasma generated body force, bypass transition on the aerofoil surface is delayed.

Direct simulation of sound generation by a two-dimensional flow past a wedge

Direct simulations of sound generation due to two-dimensional, unsteady, laminar flow past a wedge at several angles of incidence have been performed using a highly accurate, physical dispersion relation preserving scheme. We have considered a uniform flow past a wedge at a Mach number of M = 0.2 and a Reynolds number of Re = 100, at thirteen different angles of incidence 0° ≤ α ≤ 60°. Results show that the vortex shedding phenomena which in turn strongly depend on the angle of incidence are responsible for triggering negative and positive pressure pulses. We have in particular focused our attention on a special case α = 30° where the mean drag attains a lowest value among all angle of incidence cases and also reports a highest root mean square value for the lift coefficient. We have closely related the effects of the fluctuations in flow field parameters on the frequency and amplitudes of generated sound waves. The generated sound field displays dipolar nature. The lift dipole contributes more to the sou...