Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient

A characteristic of Bennett's acceptance ratio method

A powerful and well-established tool for free-energy estimation is Bennett's acceptance ratio method. Central properties of this estimator, which employs samples of work values of a forward and its time reversed process, are known: for given sets of measured work values, it results in the best estimate of the free-energy difference in the large sample limit. Here we state and prove a further characteristic of the acceptance ratio method: the convexity of its mean square error. As a two-sided estimator, it depends on the ratio of the numbers of forward and reverse work values used. Convexity of its mean square error immediately implies that there exists an unique optimal ratio for which the error becomes minimal. Further, it yields insight into the relation of the acceptance ratio method and estimators based on the Jarzynski equation. As an application, we study the performance of a dynamic strategy of sampling forward and reverse work values

Axiomatic Attribution for Multilinear Functions

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a standard cost sharing model. Second, we show that there is a unique attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity, Affine Scale Invariance, and Anonymity for all characteristic functions that are the sum of a multilinear function and an additive function. We term this the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness result does not hold for characteristic functions outside this class. Third, we study multilinear characteristic functions in detail; we describe a computationally efficient implementation of the Aumann-Shapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.Comment: 21 pages, 2 figures, updated version for EC '1

Recovering Epipolar Geometry from Images of Smooth Surfaces

We present four methods for recovering the epipolar geometry from images of smooth surfaces. In the existing methods for recovering epipolar geometry corresponding feature points are used that cannot be found in such images. The first method is based on finding corresponding characteristic points created by illumination (ICPM - illumination characteristic points' method (PM)). The second method is based on correspondent tangency points created by tangents from epipoles to outline of smooth bodies (OTPM - outline tangent PM). These two methods are exact and give correct results for real images, because positions of the corresponding illumination characteristic points and corresponding outline are known with small errors. But the second method is limited either to special type of scenes or to restricted camera motion. We also consider two more methods which are termed CCPM (curve characteristic PM) and CTPM (curve tangent PM), for searching epipolar geometry for images of smooth bodies based on a set of level curves with constant illumination intensity. The CCPM method is based on searching correspondent points on isophoto curves with the help of correlation of curvatures between these lines. The CTPM method is based on property of the tangential to isophoto curve epipolar line to map into the tangential to correspondent isophoto curves epipolar line. The standard method (SM) based on knowledge of pairs of the almost exact correspondent points. The methods have been implemented and tested by SM on pairs of real images. Unfortunately, the last two methods give us only a finite subset of solutions including "good" solution. Exception is "epipoles in infinity". The main reason is inaccuracy of assumption of constant brightness for smooth bodies. But outline and illumination characteristic points are not influenced by this inaccuracy. So, the first pair of methods gives exact results.Comment: accepted to "Pattern Recognition and Image Analysis" for publishing in 2013, 33 pages, 19 figure

Acceleration of convergence characteristic of the ICCG method

The effectiveness of renumbering for the incomplete Cholesky conjugate gradient (ICCG) solver, which is usually applied to direct solvers, is examined quantitatively by analyzing 3D standard benchmark models. On an acceleration factor which is introduced to obtain convergence quickly, indices for determining the optimum value of the acceleration factor, which minimizes the number of iterations, are discussed. It is found that the renumbering is effective to use with the ICCG solver, and the solver using the acceleration factor gives a good convergence characteristic even in the case when the conventional solver fails to provide convergent solutions</p

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Aeroacoustics simulations require much more precise boundary conditions than classical aerodynamics. Two classes of non-reflecting boundary conditions for aeroacoustics are compared in the present work: characteristic analysis based methods and Tam and Dong approach. In characteristic methods, waves are identified and manipulated at the boundaries while Tam and Dong use modified linearized Euler equations in a buffer zone near outlets to mimic a non-reflecting boundary. The principles of both approaches are recalled and recent characteristic methods incorporating the treatment of transverse terms are discussed. Three characteristic techniques (the original NSCBC formulation of Poinsot and Lele and two versions of the modified method of Yoo and Im) are compared to the Tam and Dong method for four typical aeroacoustics problems: vortex convection on a uniform flow, vortex convection on a shear flow, acoustic propagation from a monopole and from a dipole. Results demonstrate that the Tam and Dong method generally provides the best results and is a serious alternative solution to characteristic methods even though its implementation might require more care than usual NSCBC approaches