Hybrid atomistic-continuum formulations for gaseous flows

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2003.Includes bibliographical references (p. 147-156).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Hybrid atomistic-continuum formulations allow the simulation of complex hydrodynamic phenomena at the nano and micro scales without the prohibitive cost of a fully atomistic approach. This is achieved through a domain decomposition strategy whereby the atomistic model is limited to regions of the flow field where required and the continuum model is implemented side-by-side in the remainder of the domain within a single computational framework. The current work is focused on arguably the most critical elements of any hybrid formulation: the atomistic-continuum coupling method and the imposition of continuum boundary conditions on the atomistic subdomain. The relative merits of different approaches for both are delineated and demonstrated using sample test problems. For the case of incompressible steady gaseous flows a hybrid formulation is developed using a finite element method for the continuum subdomain and the direct simulation Monte Carlo (DSMC) method for the atomistic subdomain. The Schwarz alternating method is used to couple both subdomains using an overlap region across which the successive exchange of Dirichlet boundary conditions yields a steady state solution. This approach has the advantages of decoupling both length scales and time scales of the atomistic and continuum solvers leading to superior performance over conventional explicit schemes. Continuum boundary conditions are imposed on the atomistic subdomain using the Chapman-Enskog distribution function in conjunction with particle reservoirs. A driven cavity test problem shows convergence in 0(10) Schwarz iterations for flow Reynolds numbers 0(1).(cont.) The Schwarz method is also, for the first time, extended to couple unsteady hybrid incompressible flows. Tests for an impulsively driven Couette flow highlight the versatility of this approach to advance solutions to arbitrary times through appropriate interpolation of Dirichlet boundary conditions. Techniques are also developed using limited ensemble averaging of the atomistic solution to realize significant computational savings over a standard ensemble averaging process while maintaining the same variance reduction. Finally an unsteady compressible hybrid formulation utilizing Adaptive Mesh and Algorithm Refinement (AMAR) technology is described. DSMC is used to model the atomistic regions on the finest grid of the adaptive hierarchy. The continuum flow is solved using a second order Godunov scheme. New gradient-based tolerance parameters are developed to provide robust detection and tracking of concentration diffusion fronts and stationary and moving shock waves. Extension of AMAR to binary gas mixtures is also completed and demonstrated using a binary gas shock wave test problem.by Hettithanthrige Sanith Wijesinghe.Ph.D

Aerodynamic response of turbomachinery blade rows to convecting density wakes

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1998.Includes bibliographical references (p. 129-131).Density wakes have been recently identified as a possible new source for high cycle fatigue failure in the compressor blades of modern turbomachinery. In order to characterize the density wake induced force and moment fluctuations in compressor blades a two-dimensional computational study has been conducted in viscous compressible flows with Mach numbers ranging from M[infinity], = 0.15 to M[infinity] = 0.87 and flow Reynolds number Re(c, U[infinity]) ~~700,000. Parametric tests were conducted at each flow Mach number to establish trends for the change in the maximum fluctuation of the blade force and moment coefficients with the changes in the density wake width 0.1 < w/c < 1.0 and the density ratio 0.25 < P2/P1 < 2.0. Results indicate the magnitude of the blade force and moment fluctuations to scale with (1) the non-dimensional density wake width w/c, (2) a non-dimensional density parameter p* and (3) flow Mach number M[infinity]. The viscous flow simulations have also indicated (1) periodic vortex shedding at the blade trailing edge and (2) separation bubbles on the blade suction surface which generate additional force and moment fluctuations with amplitudes ±(10 - 100%) about the time averaged mean values. These flow features represent possible additional sources for high cycle fatigue failure. Simple functional relationships have also been derived at each flow Mach number to quantify the force and moment fluctuations described above. In addition a simple cascade flow model has been developed in conjunction with the computational study to help determine the trends in the force and moment fluctuations with varying density wake properties and compressor geometries.by Hettithanthrige Sanith Wijesinghe.S.M

Detecting tax evasion: a co-evolutionary approach

We present an algorithm that can anticipate tax evasion by modeling the co-evolution of tax schemes with auditing policies. Malicious tax non-compliance, or evasion, accounts for billions of lost revenue each year. Unfortunately when tax administrators change the tax laws or auditing procedures to eliminate known fraudulent schemes another potentially more profitable scheme takes it place. Modeling both the tax schemes and auditing policies within a single framework can therefore provide major advantages. In particular we can explore the likely forms of tax schemes in response to changes in audit policies. This can serve as an early warning system to help focus enforcement efforts. In addition, the audit policies can be fine tuned to help improve tax scheme detection. We demonstrate our approach using the iBOB tax scheme and show it can capture the co-evolution between tax evasion and audit policy. Our experiments shows the expected oscillatory behavior of a biological co-evolving system

Modeling tax evasion with genetic algorithms

The U.S. tax gap is estimated to exceed $450 billion, most of which arises from non-compliance on the part of individual taxpayers (GAO 2012; IRS 2006). Much is hidden in innovative tax shelters combining multiple business structures such as partnerships, trusts, and S-corporations into complex transaction networks designed to reduce and obscure the true tax liabilities of their individual shareholders. One known gambit employed by these shelters is to offset real gains in one part of a portfolio by creating artificial capital losses elsewhere through the mechanism of “inflated basis” (TaxAnalysts 2005), a process made easier by the relatively flexible set of rules surrounding “pass-through” entities such as partnerships (IRS 2009). The ability to anticipate the likely forms of emerging evasion schemes would help auditors develop more efficient methods of reducing the tax gap. To this end, we have developed a prototype evolutionary algorithm designed to generate potential schemes of the inflated basis type described above. The algorithm takes as inputs a collection of asset types and tax entities, together with a rule-set governing asset exchanges between these entities. The schemes produced by the algorithm consist of sequences of transactions within an ownership network of tax entities. Schemes are ranked according to a “fitness function” (Goldberg in Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Boston, 1989); the very best schemes are those that afford the highest reduction in tax liability while incurring the lowest expected penalty.Mitre Corporation (Innovation Program

Detecting tax evasion: a co-evolutionary approach

We present an algorithm that can anticipate tax evasion by modeling the co-evolution of tax schemes with auditing policies. Malicious tax non-compliance, or evasion, accounts for billions of lost revenue each year. Unfortunately when tax administrators change the tax laws or auditing procedures to eliminate known fraudulent schemes another potentially more profitable scheme takes it place. Modeling both the tax schemes and auditing policies within a single framework can therefore provide major advantages. In particular we can explore the likely forms of tax schemes in response to changes in audit policies. This can serve as an early warning system to help focus enforcement efforts. In addition, the audit policies can be fine tuned to help improve tax scheme detection. We demonstrate our approach using the iBOB tax scheme and show it can capture the co-evolution between tax evasion and audit policy. Our experiments shows the expected oscillatory behavior of a biological co-evolving system