Multicomponent mixing on the “diffusion – convection” transition boundary at elevated pressures

An experimental and theoretical study of three-component mixing at the “diffusion – convection” boundary at elevated pressures is carried out. It is shown that the pressure dependence of the dimensionless parameter α, defined as the ratio of the experimental values of the component concentrations to those calculated by the Stefan-Maxwell equations, has characteristic regions due to the interaction of structural formations moving towards each other, in which a transition from one critical motion to another occurs. Within the framework of a linear analysis of the stability of a ternary gas mixture for a vertical circular cylinder channel, it is shown that scale perturbations determining the transition from one type of flow to another correspond to a certain value of the perturbation mode n and the critical Rayleigh numbers.

Parallel algorithms for solving diffusion-convection problems on a multiprocessor computer system using hybrid MPI / OpenMP technology

The paper deals with the mathematical models, algorithms and software for mathematical modeling of coastal systems’ water pollution spreading dynamics under various unfavorable phenomena of natural and artificial genesis, developed for high-performance cluster systems. Methods for partitioning the computational domain for solving diffusion-convection problems have been developed, which allow for efficient parallelization of a computationally complex modeling problem, taking into account the architecture of the multiprocessor system used. The developed mathematical models are based on high-precision models of hydrophysics and hydrobiology and take into account the peculiarities of water systems in the south of the Rostov region, as well as factors of hydrobiological dynamics such as microturbulent diffusion and advective transport in various directions, mechanisms of primary and secondary pollution of coastal systems, taking into account currents. The paper presents algorithms for solving a simulated problem based on MPI parallelization technology, as well as based on mixed MPI + OpenMP technology. Numerical experiments have been carried out and the two technologies efficiency comparison has been made in the conditions of computing cluster used.

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated L2 error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.

Numerical Simulation for Unsteady Anisotropic-Diffusion Convection Equation of Spatially Variable Coefficients and Incompressible Flow

The anisotropic-diffusion convection equation of spatiallyvariable coefficients which is relevant for functionally graded mediais discussed in this paper to find numerical solutions by using acombined Laplace transform and boundary element method. The variablecoefficients equation is transformed to a constant coefficients equation.The constant coefficients equation is then Laplace-transformed sothat the time variable vanishes. The Laplace-transformed equationis consequently written in a pure boundary integral equation whichinvolves a time-free fundamental solution. The boundary integral equationis therefore employed to find numerical solutions using a standardboundary element method. Finally the results obtained are inverselytransformed numerically using the Stehfest formula to get solutionsin the time variable. The combined Laplace transform and boundaryelement method is easy to be implemented, efficient and accurate forsolving unsteady problems of anisotropic functionally graded mediagoverned by the diffusion convection equation.

Combining Diffusion, Convection and Absorption: A Pilot Study of Polymethylmethacrylate versus Polysulfone Membranes in the Removal of P-Cresyl Sulfate by Postdilution On-Line Hemodiafiltration

Dialytic clearance of p-cresyl sulfate (pCS) and other protein-bound toxins is limited by diffusive and convective therapies, and only a few studies have examined how to improve their removal by adsorptive membranes. This study tested the hypothesis that high-flux polymethylmethacrylate (PMMA) dialysis membranes with adsorptive capacity increase pCS removal compared to polysulfone membranes, in a postdilution on-line hemodiafiltration (OL-HDF) session. Thirty-five stable hemodialysis patients randomly completed a single study of 4 h OL-HDF with PMMA (BG2.1U, Toray®, Tokyo, Japan) and polysulfone (TS2.1, Toray®) membranes. The primary endpoint was serum pCS reduction ratios (RRs) obtained with each dialyzer. Secondary outcomes included RRs of other solutes such as β2-microglobulin, the convective volume obtained after each dialysis session, and the dialysis dose estimated by ionic dialysance (Kt) and urea kinetics (Kt/V). The RRs for pCS were higher with the PMMA membrane than those obtained with polysulfone membrane (88.9% vs. 58.9%; p < 0.001), whereas the β2-microglobulin RRs (67.5% vs. 81.0%; p < 0.001), Kt (60.2 ± 8.7 vs. 65.5 ± 9.4 L; p = 0.01), Kt/V (1.9 ± 0.4 vs. 2.0 ± 0.5; p = 0.03), and the convection volume (18.8 ± 2.8 vs. 30.3 ± 7.8 L/session; p < 0.001) were significantly higher with polysulfone membrane. In conclusion, pCS removal by OL-HDF was superior with high-flux PMMA membranes, appearing to be a good dialysis strategy for improving dialytic clearance of pCS, enabling an acceptable clearance of β2-microglobulin and small solutes.

Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

On the minimal residual methods for solving diffusion-convection SLAEs

The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA — orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT — preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.