Showing papers by "Alexander Kurganov published in 2022"

Well-Balancing via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts

Abstract: We study the flux globalization based central-upwind scheme from Cheng et al. (J Sci Comput 80:538–554, 2019) for the Saint-Venant system of shallow water equations. We first show that while the scheme is capable of preserving moving-water equilibria, it fails to preserve much simpler “lake-at-rest” steady states. We then modify the computation of the global flux variable and develop a well-balanced scheme, which can accurately handle both still- and moving-water equilibria. In addition, we extend the flux globalization based central-upwind scheme to the case when “dry” and/or “almost dry” areas are present. To this end, we introduce a hybrid approach: we use the flux globalization based scheme inside the “wet” areas only, while elsewhere we apply the central-upwind scheme from Bollermann et al. (J Sci Comput 56:267–290, 2013), which is designed to accurately capture wet/dry fronts. We illustrate the performance of the proposed schemes on a number of numerical examples.

Influence of High-Molecular n-Alkane Associates on Rheological Behavior of the Crude Oil Residue

Abstract: In this paper, we present the results of chemical and physical investigations of the crude oil residue of low-sulfur but high-paraffin-base crude oil produced from the Mangyshlak (Kazakhstan) reservoir. The object contains 14.6 wt % of resins and significant amounts of high-molecular alkanes. A non-Newtonian behavior of the system is preserved even at 70–90 °C. 1H NMR data revealed divergence in temperature-dependent ratios corresponding to the low-viscous liquid petroleum products. The experimental results indicate the existence of associations of n-alkanes among themselves, as well as with resins and asphaltenes in the composition of the crude oil residue sample. In paraffin-base crude oil, the size of such associates (coacervates) is in the range of 100–300 nm. The associative behavior of medium- and long-chain n-alkanes is explained by their existence in transitional plastic (rotator) phases. As building blocks, associates of n-alkanes can be combined into worm-like structures due to adsorption of resins and asphaltenes on their surface and adhesion, thereby determining the non-Newtonian behavior and thixotropy of the system. Worm-like structures may be partially destructed under shear thinning (torn into shorter pieces) but can regenerate their structure over time. The optical and electron microscopy results justify the asphaltene aggregation model proposed by Balestrin and Loh. The formation of coacervates from asphaltene and concomitant molecules, which are surrounded by solvation shells of high-molecular alkanes, is evidenced. It is proposed that high-molecular n-alkane associates, as well as coacervates containing asphaltene and concomitant molecules, are compositional parts of many oil dispersed systems.

A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography

Abstract: We consider the two-dimensional rotating shallow water equations with nonflat bottom topography. We focus on the case of low Froude number, in which the system is stiff and conventional explicit numerical methods are extremely inefficient and often impractical. Our goal is to design a finite volume scheme, which is both asymptotic preserving (uniformly asymptotically consistent and stable for a broad range of low Froude numbers) and well-balanced (capable of exactly preserving geophysically relevant steady-state solutions). The goal is achieved in two steps. We first rewrite the studied equations in terms of perturbations of the steady state and then apply the flux splitting similar to the one used in [Liu, Chertok, and Kurganov J. Comput. Phys., 391 (2019), pp. 259-279]. We split the flux into the stiff and nonstiff parts and then use an implicit-explicit approach: apply an explicit second-order central-upwind scheme to the nonstiff part of the system while treating the stiff part implicitly. As the stiff part of the flux is linear, we reduce the implicit stage of the proposed method to solving a Poisson-type elliptic equation, which is discretized using a standard second-order central difference scheme. We prove the asymptotic preserving property of the developed scheme and conduct a series of numerical experiments, which demonstrate that our scheme outperforms the non-well-balanced asymptotic preserving scheme from [Liu, Chertok, and Kurganov J. Comput. Phys., 391 (2019), pp. 259-279].

Reuse of low sulfur oil residues as a base for boiler and marine fuel

Abstract: THE PURPOSE. A complex of various physico-chemical methods has been studied to explore the possibilities of reuse of oil residues (oil sludge) of low-sulfur high-paraffin oil deposits of the Mangyshlak peninsula (Kazakhstan) as a promising raw material for boiler and marine fuel with improved operational and environmental characteristics.METHODS. Determination of the conditional viscosity of oil sludge (in degrees Engler, ° E) was carried out using an Engler viscometer VU-M-PCP according to GOST 6258-85 «Petroleum products. The method of determining the conditional viscosity». Studies of the lowest working heat of combustion of oil sludge were carried out using an adiabatic bomb calorimeter ABK-1B (Russia) according to GOST 21261-91 "Petroleum products. Method for determining the highest heat of combustion and calculation of the lowest heat of combustion". Determination of the mass fraction of sulfur in the studied oil sludge was also carried out using an adiabatic bomb calorimeter ABK-1B (Russia) according to GOST 3877-88 «Petroleum products. Method of determination of sulfur by burning in a calorimetric bomb». To analyze the results obtained, data obtained using the nuclear magnetic resonance method were used. Proton NMR spectra were recorded on a Bruker AVANCE III NMR spectrometer operating at a frequency of 600.13 MHz for 1H and equipped with a highresolution inverse sensor for three cores (TXI, 5 mm). Data processing and analysis were performed using Bruker Topspin 3.6.1.RESULTS. It is shown that in terms of heat of combustion and viscosity properties at temperatures above 50 oC, this oil sludge is similar to boiler fuel oil M100. It was found that the use of carbonate sludge of chemical water treatment at a concentration of 0.1 wt. % allows you to further reduce the viscosity by 5-6% and reduce the sulfur content in the combustion products, without reducing the lower working heat of combustion of the oil product. The complex nature of the relationship between the width of NMR lines and viscous properties has been revealed, which may indicate the existence of associates of highmolecular paraffins even in slightly viscous liquid petroleum products. The nature and characteristic sizes of the resulting associates are discussed. It is shown that the addition of medium-distillate diesel fractions will make it possible to obtain a better fuel option for marine engines, gas turbine and boiler installations with a reduced amount of resinous-asphaltene substances, reduced viscosity values and solidification temperatures, high heat of combustion and low sulfur content.СONCLUSION. The conducted complex of physico-chemical studies has shown the possibility of using low-sulfur Mangyshlak oil sludge as a basis for obtaining fuel for marine engines, gas turbine and boiler plants, steam boilers and industrial furnaces.

Predicting the Potentiometric Sensitivity of Membrane Sensors Based on Modified Diphenylphosphoryl Acetamide Ionophores with QSPR Modeling

Abstract: While potentiometric, plasticized membrane sensors are known as convenient, portable and inexpensive analytical instruments, their development is time- and resource-consuming, with a poorly predictable outcome. In this study, we investigated the applicability of the QSPR (quantitative structure–property relationship) method for predicting the potentiometric sensitivity of plasticized polymeric membrane sensors, using the ionophore chemical structure as model input. The QSPR model was based on the literature data on sensitivity, from previously studied, structurally similar ionophores, and it has shown reasonably good metrics in relating ionophore structures to their sensitivities towards Cu2+, Cd2+ and Pb2+. The model predictions for four newly synthesized diphenylphosphoryl acetamide ionophores were compared with real potentiometric experimental data for these ionophores, and satisfactory agreement was observed, implying the validity of the proposed approach.

A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics

Abstract: We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses several important properties: it locally preserves the divergence-free constraint, it does not rely on any (approximate) Riemann problem solver, and it robustly produces high-resolution and non-oscillatory results. The derivation of the scheme is based on the Godunov-Powell nonconservative modifications of the studied MHD systems. The local divergence-free property is enforced by augmenting the modified systems with the evolution equations for the corresponding derivatives of the magnetic field components. These derivatives are then used to design a special piecewise linear reconstruction of the magnetic field, which guarantees a non-oscillatory nature of the resulting scheme. In addition, the proposed PCCU discretization accounts for the jump of the nonconservative product terms across cell interfaces, thereby ensuring stability. We test the proposed PCCU scheme on several benchmarks for both ideal and shallow water MHD systems. The obtained numerical results illustrate the performance of the new scheme, its robustness, and its ability not only to achieve high resolution, but also preserve the positivity of computed quantities such as density, pressure, and water depth.

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Abstract: We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind numerical fluxes, the three-stage third-order strong stability preserving Runge-Kutta time integrator, and the fifth-order WENO-Z interpolation. The adaptive strategy is implemented by applying the limited interpolation only in the parts of the computational domain where the solution is identified as ``rough'' with the help of a smoothness indicator. We develop and use a new simple and robust local smoothness indicator (LSI), which is applied to the solutions computed at each of the three stages of the ODE solver. The new LSI and adaptive A-WENO schemes are tested on the Euler equations of gas dynamics. We implement the proposed LSI using the pressure, which remains smooth at contact discontinuities, while our goal is to detect other ``rough'' areas and apply the limited interpolation mostly in the neighborhoods of the shock waves. We demonstrate that the new adaptive schemes are highly accurate, non-oscillatory, and robust. They outperform their fully limited counterparts (the A-WENO schemes with the same numerical fluxes and ODE solver but with the WENO-Z interpolation employed everywhere) while being less computationally expensive.

A Diffuse-Domain Based Numerical Method for a Chemotaxis-Fluid Model

Abstract: In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biological chemotaxis phenomenon in the fluid environment and couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force, which is proportional to the relative surplus of the cell density compared to the water density. We develop a new positivity preserving and high-resolution method for the studied chemotaxis-fluid system. Our method is based on the diffuse-domain approach, which we use to derive a new chemotaxis-fluid diffuse-domain (cf-DD) model for simulating bioconvection in complex geometries. The drop domain is imbedded into a larger rectangular domain, and the original boundary is replaced by a diffuse interface with finite thickness. The original chemotaxis-fluid system is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the physical interface. We show that the cf-DD model converges to the chemotaxis-fluid model asymptotically as the width of the diffuse interface shrinks to zero. We numerically solve the resulting cf-DD system by a second-order hybrid finite-volume finite-difference method and demonstrate the performance of the proposed approach on a number of numerical experiments that showcase several interesting chemotactic phenomena in sessile drops of different shapes, where the bacterial patterns depend on the droplet geometries.