THEORETICAL MATHEMATICAL MODELING OF HEAT EXCHANGE IN PIPES WITH TRIANGULAR AND SQUARE TURBULATORS WITH d/D=0.95÷0.90, t/D=0.25÷1.00 AND HIGH REYNOLDS NUMBERS Re=106

Mathematical modeling of heat exchange process in straight and round horizontal pipes with protrusions and d/D=0.95...0.90, t/D=0.25...1.00 of triangular and square sections with large Reynolds numbers (RE=106) are carried out on the basis of multiblock computing technologies based on solutions of factored and finite-volume algorithm of RANS equations and energy equations. It is shown that for higher square protrusions and at higher Reynolds numbers, a limited increase in NU/NUgl is accompanied by a significant increase in relative hydro resist ance in accordance with the higher Reynolds number; for triangular turbulators, this persists and even deepens.

An explicit finite volume algorithm for vanishing viscosity solutions on a network

<p style='text-indent:20px;'>In [Andreianov, Coclite, Donadello, Discrete Contin. Dyn. Syst. A, 2017], a finite volume scheme was introduced for computing vanishing viscosity solutions on a single-junction network, and convergence to the vanishing viscosity solution was proven. This problem models <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula> incoming and <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> outgoing roads that meet at a single junction. On each road the vehicle density evolves according to a scalar conservation law, and the requirements for joining the solutions at the junction are defined via the so-called vanishing viscosity germ. The algorithm mentioned above processes the junction in an implicit manner. We propose an explicit version of the algorithm. It differs only in the way that the junction is processed. We prove that the approximations converge to the unique entropy solution of the associated Cauchy problem.</p>

Fast deep swept volume estimator

Despite decades of research on efficient swept volume computation for robotics, computing the exact swept volume is intractable and approximate swept volume algorithms have been computationally prohibitive for applications such as motion and task planning. In this work, we employ deep neural networks (DNNs) for fast swept volume estimation. Since swept volume is a property of robot kinematics, a DNN can be trained off-line once in a supervised manner and deployed in any environment. The trained DNN is fast during on-line swept volume geometry or size inferences. Results show that DNNs can accurately and rapidly estimate swept volumes caused by rotational, translational, and prismatic joint motions. Sampling-based planners using the learned distance are up to five times more efficient and identify paths with smaller swept volumes on simulated and physical robots. Results also show that swept volume geometry estimation with a DNN is over 98.9% accurate and 1,200 times faster than an octree-based swept volume algorithm.

Solving Capacitated Facility Location Problem Using Lagrangian Decomposition and Volume Algorithm

In this research, we will focus on one variant of the problem: the capacitated facility location problem (CFLP). In many formulations of the CFLP, it is assumed that each demand point can be supplied by only one open facility, which is the simplest case of the problem. We consider the case where each demand point can be supplied by more than one open facility. We first investigate a Lagrangian relaxation approach. Then, we illustrate in the problem decomposition how to introduce tighter constraints, which solve the CFLP faster while achieving a better quality solution as well. At the same time, we apply the volume algorithm to improve both the lower and the upper bound on the optimum solution of the original problem for the large problem size.