M. Ramakrishna

A Fast, Two-Dimensional Panel Method

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. In this paper the method is modified to improve computational efficiency by adapting the fast multipole algorithm for the panel method. Significant improvement in computational efficiency is obtained while ensuring that the edge effects are eliminated.

Determination of unsteady heat release distribution from acoustic pressure measurements: A reformulation of the inverse problem

An integral method is developed to solve the inverse problem of determining the oscillatory heat release distribution from the knowledge of the acoustic pressure field within a combustor. Unlike earlier approaches, in which the problem is formulated in terms of Fredholm integral equation, the inverse problem is reformulated in terms of Volterra integral equation. This reformulation, valid for low Mach numbers (M2 << 1), facilitates the recovery of heat release at all frequencies. The resulting Volterra integral equation is solved using both direct numerical method and implicit least-squares method. The results show that the implicit least-squares method is superior to the direct numerical method and yields accurate determination of heat release at all frequencies.

Efficient random walks in the presence of complex two-dimensional geometries

This paper details an efficient algorithm for particles undergoing random walks in the presence of complex, two-dimensional, solid boundaries. The scheme is developed for the simulation of vortex diffusion using the random vortex method. Both vortex blobs and sheets are handled. The relevant modifications for using the algorithm with the vorticity redistribution technique are also discussed. The algorithm is designed to be used in the framework of an existing fast multipole implementation. A measure for the geometric complexity of a body is introduced and the algorithms efficiency is studied as various parameters are changed for bodies of varying complexity.

Computation of noise spectral density in switched capacitor circuits using the mixed-frequency-time technique

A time-domain algorithm for computation of the noise power spectral density (PSD) is proposed by V. Vasudevan. When applied to periodically varying circuits, this formulation requires efficient methods to obtain the quasi-periodic steady-state solution of a set of linear time-varying ordinary differential equations. We use both the mixed frequency-time technique (MFT) and the shooting Newton method for this computation. We show that, at each frequency for which the spectral density is sought, MFT requires only two integrations over the duration of the clock period. The results are compared with published experimental and computed data.

Computation of the average and harmonic noise power-spectral density in switched-capacitor circuits

Switched-capacitor (SC) circuits are periodically time-varying circuits and the noise at the output of these circuits is cyclostationary. This noise is therefore characterized by the average and harmonic spectral densities. We extend the method proposed in a previous paper to compute the average and harmonic noise-spectral densities in periodically varying circuits. We derive expressions for the average and harmonic spectral densities and use the mixed-frequency-time technique for the computation. The results for the average spectral density are compared with published results. The contribution of the harmonic spectral densities to the average noise-spectral density at the output of a cascaded block is estimated.

A transistor level placement tool for custom cell generation

In this paper, we present a transistor level placer suitable for the macro cell design style. The Eulerian path finding algorithm is used to create locally optimal placements of groups of transistors, called stacks. Typically however there are large disparities in the sizes of the various stacks obtained. It is therefore not always possible to meet the desired cell aspect ratio/height/width specifications. In our placer, these stacks can be reshaped so that the constraints on the cell are met. The optimisation tool used is simulated annealing. Placements for cells containing several hundred transistors were generated using this method.

An efficient algorithm for frequency-weighted balanced truncation of VLSI interconnects in descriptor form

Balanced truncation of descriptor systems requires computation of spectral projectors and solution of the generalized projected Lyapunov equations, both of which have significant complexity. Frequency-weighted balancing methods are more efficient if the response over a specific frequency range is desired. However, a direct extension of these methods to descriptor systems requires the spectral projectors. In this paper, we propose an efficient frequency-weighted balanced truncation algorithm without finding the spectral projectors. Samples of the frequency-domain solution to the system are used to get an accurate estimate of the improper Gramians. The proper Gramians are computed after adjusting for the contribution of the improper subsystem. Low rank factors of these Gramians are used to obtain a basis that includes the contribution of both the proper and improper subsystems. Congruence transform is used to ensure passivity of RLC interconnect models. Results for standard benchmarks show that the method is accurate and efficient.

Improvement of High Alpha Aerodynamics for Compound Delta Wing Aircraft Using Leading Edge Vortex Controller

An experimental and numerical investigation of high alpha aerodynamics is reported for a generic compound delta wing fighter aircraft configuration in transonic Mach number regime. The aircraft considered here is a wing-fuselage-vertical fin tailless compound delta configuration with lower inboard and higher outboard sweeps and a close combat missile outboard. The basic configuration does not have any leading or trailing edge devices such as slats and flaps. This configuration is studied first to understand the flow physics causing pitch up phenomenon for the basic configuration. Subsequently, the use of leading edge vortex controller (LEVCON) is studied for controlling pitch up. Both Computational Fluid Dynamics (CFD) and wind tunnel experiments have been used to describe the flow physics.

A new multigrid algorithm for non-linear equations in conjunction with time-marching procedures

Full approximate storage (FAS) multigrid algorithm is the most commonly used multigrid algorithm for non-linear equations. The algorithm initially developed for steady-state equations was later extended to obtain steady-state solutions employing unsteady equations. In extending the FAS algorithm for the steady-state non-linear equations to unsteady non-linear equations, the FAS algorithm does not to take into account that the governing equations are typically linearized in time before they are solved. Thus, there is a scope to develop a new multigrid algorithm to apply the multigrid technique to the equations linearized in time. In the present work, such an algorithm is developed exploring this possibility and is implemented for two-dimensional incompressible and compressible flows coupled with explicit time marching procedures. The results of the new algorithm compare favourably with those of the FAS multigrid method and single grid.

DETERMINATION OF UNSTEADY HEAT RELEASE DISTRIBUTION FROM ACOUSTIC PRESSURE MEASUREMENTS

An integral method is developed to solve the inverse problem of determining the oscillatory heat release distribution from the knowledge of the acoustic pressure field within a combustor. Unlike earlier approaches, in which the problem is formulated in terms of Fredholm integral equation, the inverse problem is reformulated in terms of Volterra integral equation. This reformulation facilitates the recovery of heat release at all frequencies. The resulting Volterra integral equation is solved using both direct numerical method ( DNM) and implicit least squares method ( ILSM). The results show that the implicit least squares method is superior to the direct numerical method and yields accurate determination of heat release at all frequencies.