Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [ P. Asinari and I. V. Karlin Phys. Rev. E 79 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed

Aerothermal modeling program, phase 2

The main objectives of the Aerothermal Modeling Program, Phase 2 are: to develop an improved numerical scheme for incorporation in a 3-D combustor flow model; to conduct a benchmark quality experiment to study the interaction of a primary jet with a confined swirling crossflow and to assess current and advanced turbulence and scalar transport models; and to conduct experimental evaluation of the air swirler interaction with fuel injectors, assessments of current two-phase models, and verification the improved spray evaporation/dispersion models

Mathematical Models in Management Sciences. (1) - Consumer Behaviour as a Markov Process

Mathematical models based on Markov processes for consumer purchasing behavio

Numerical investigation of oil injection in a Roots blower operated as expander

The adoption of positive displacement machines as expanders in Organic Rankine Cycles (ORCs) is increasingly common, especially in the low to medium power range. At the same time, these devices often serve as compressor in Vapor-Compression Refrigeration Systems. In both cases, the application of Computation Fluid Dynamics (CFD) to optimize such machines has become an integrated tool in the design process. As a consequence, several challenges associated with the numerical simulation have to be taken into account. For example, the modeling of the gap represents a challenge for the stability of the numerical analysis. The dynamic of the process, combined with deformations of the clearances and of the working chamber has to be considered with extra care. To raise the efficiency of the machine, oil is typically injected. Its numerical modeling imply an extra challenge in the simulation of the actual operation of the machine. The present work is mainly focused on the multi-phase nature of the flow, with a particular analysis of the lubricant oil injected. In this work, a two-lobe Roots blower operated as expander has been simulated with the open-source software OpenFOAM-v1812, using the SCORG-V5.2.2. This analysis highlights the areas that are affected the most by the oil presence in order to highlight the sealing effect it provides

Using Elimination Theory to construct Rigid Matrices

The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an n x n matrix in this family are distinct primitive roots of unity of orders roughly exp(n^2 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination theory of polynomial ideals. In particular, we use results on the existence of polynomials in elimination ideals with effective degree upper bounds (effective Nullstellensatz). Using elementary algebraic geometry, we prove that the dimension of the affine variety of matrices of rigidity at most k is exactly n^2-(n-r)^2+k. Finally, we use elimination theory to examine whether the rigidity function is semi-continuous.Comment: 25 Pages, minor typos correcte

Finite volume solutions for electromagnetic induction processing

A new method is presented for numerically solving the equations of electromagnetic induction in conducting materials using native, primary variables and not a magnetic vector potential. Solving for the components of the electric field allows the meshed domain to cover only the processed material rather than extend further out in space. Together with the finite volume discretisation this makes possible the seamless coupling of the electromagnetic solver within a multi-physics simulation framework. After validation for cases with known results, a 3-dimensional industrial application example of induction heating shows the suitability of the method for practical engineering calculation