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1

Finite Volume Method for the Combustion Reaction of Energetic Materials

Yu Yanchun, Fu Qiang, Ma Jingxin, Chen Weidong, Yan Han

Central European Journal of Energetic Materials

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2023

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Vol. 20, no. 2

159--199

EN

In order to analyse the effects of launch on the internal structure due to launch and given the relative paucity of experimental tests in this regime numerical simulations are an important method of prediction. Viscoelastic statistical crack mechanics offer a solution to the dynamic damage problems of explosives involved in explosion, impact and collision. Most finite element software does not include a viscoelastic statistical crack constitutive model; the model can only be embedded in the finite element software. Therefore, a computer program based on the finite volume method combined with viscoelastic statistical crack mechanics is presented, aiming to analyze the explosion problems more precisely and conveniently. A combustion equation of state is proposed to study the combustion reaction of explosives; the trends of temperature and stress of explosive during the combustion process are studied; Hot spot zones formed inside explosives are analyzed. The results are in accordance with the reaction law of combustion. The results indicate that when the bottom of the explosive charge is heated to a certain temperature, the explosive charge have a combustion reaction occurs. This conclusion has important value for studying the effect of the base gap on the launch safety of explosive munitions.

2

Experimental and numerical analyses of airflow around two cylinders angled to the direction of wind

Padewska-Jurczak Agnieszka, Szczepaniak Piotr, Walentyński Ryszard

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 1

art. no. e144578

EN

The analyses aim to determine aerodynamic force coefficients in the case of airflow around two smooth or rough cylinders positioned at different angles to the direction of wind velocity. Such systems, for instance, may be part of a tubular water slide. The results were compared with the values of the interference coefficient of the cylinders arranged in a row included in Eurocode EN 1991 part 4. The aerodynamic forces of the cylinder systems were determined on the basis of experimental tests conducted in a wind tunnel. To verify the above results, CFD (computational fluid dynamics) simulations were prepared. An important observation is that for the angle of yaw β = 0◦, the negative component of the lift force (lateral) fy is shown, while for the other cases, the situation is opposite and the lateral force points outside the gap (upward). The second is that the results of aerodynamic drag for rough cylinders arranged in a row and calculated according to EN 1991 part 4 may be underestimated. The flow around the pair of smooth cylinders is quite different from that of the rough ones, because during the experiment the first falls into the critical flow regime, while the second has supercritical characteristics.

3

Mixed convection heat transfer of a nanofluid in a square ventilated cavity separated horizontally by a porous layer and discrete heat source

Messaoud Hamdi, Adel Sahi, Ouerdia Ourrad

Archives of Thermodynamics

|

2023

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Vol. 44, no 2

87--114

EN

Laminar mixed convection heat transfer in a vented square cavity separated by a porous layer filled with different nanofluids (Fe3O4, Cu, Ag and Al2O3) has been investigated numerically. The governing equations of mixed convection flow for a Newtonian nanofluid are assumed to be two-dimensional, steady and laminar. These equations are solved numerically by using the finite volume technique. The effects of significant parameters such as the Reynolds number (10 ≤ Re ≤ 1000), Grashof number (103 ≤ Gr ≤ 106 ), nanoparticle volume fraction (0.1 ≤ φ ≤ 0.6), porous layer thickness (0 ≤ γ ≤ 1) and porous layer position (0.1 ≤ δ ≤ 0.9) are studied. Numerical simulation details are visualized in terms of streamline, isotherm contours, and average Nusselt number along the heated source. It has been shown that variations in Reynolds and Darcy numbers have an impact on the flow pattern and heat transfer within a cavity. For higher Reynolds (Re > 100), Grashof (Gr > 105 ) numbers and nanoparticles volume fractions the heat transfer rate is enhanced and it is optimal at lower values of Darcy number (Da = 10−5 ). In addition, it is noticed that the porous layer thickness and location have a significant effect on the control of the heat transfer rate inside the cavity. Furthermore, it is worth noticing that Ag nanoparticles presented the largest heated transfer rate compared to other nanoparticles.

4

Problemy dotyczące modelowania obciążenia wiatrem obiektów budowlanych

Skotniczny Krystyna, Kopernik Magdalena, Rawska-Skotniczny Anna

Materiały Budowlane

|

2022

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nr 6

63--65

PL

Im bardziej skomplikowany kształt obiektu budowlanego, tym trudniej prognozować, jak będą na niego oddziaływały masy powietrza podczas przepływu. Problem jest istotny z uwagi na niezawodność obiektów budowlanych. Analizy numeryczne oraz badania doświadczalne pozwolą w przyszłości zmodyfikować wytyczne normowe, przyczyniając się do poprawy bezpieczeństwa obiektów budowlanych.

EN

The more complex the shape of a building object, the more difficult it is to predict how air masses will affect it during flow. The problem is important for the reliability of buildings. Numerical analyses and experimental studies will allow future modification of the standard guidelines, contributing to the improvement of the safety of buildings.

5

Magnetoconvection of nanofluid in a partially heated cavity with isothermal blockage

Nagaraj Suresh, Nagarajan Nithyadevi

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

77--90

EN

Natural convection characteristics of Al2O3-water nanofluid in a cavity is investigated numerically under the influence of a inclined magnetic field. The bottom wall is partially heated, and the top wall is cooled and the remaining regions of the cavity are kept adiabatic. An isothermally heated square blockage of the different rectangular size is placed at the centre of the cavity. The schematic model is converted into mathematical form, and the non-dimensional equations are discretized by the finite volume method using power law scheme and solved by Semi-Implicit Method for Pressure Linked Equation algorithm. The relevant parameters such as Rayleigh number (104-106), Hartmann numer (10-500), size of blockage ratio (0.25-0.75), length of the heat source (0.25-1.0) and inclination angle of the magnetic field (0°-90° on the flow and temperature fields are examined. Results are presented in terms of streamlines, isotherms, velocity profile, local and average Nusselt number. It was found that for low Hartmann numbers, the average heat transfer rate attained the maximum at the inclined magnetic field of γ = 45°. In addition, the blockage ratio of B = 0.75 enhanced the higher heat transfer rate for all values of γ.

6

Simulations of Heat Transfer through Multilayer Protective Clothing Exposed to Flame

Puszkarz Adam K., Machnowski Waldemar

Autex Research Journal

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2022

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Vol. 22, no. 3

298--304

EN

In this paper, the safety and thermal comfort of protective clothing used by firefighters was analyzed. Three-dimensional geometry and morphology models of real multilayer assemblies used in thermal protective clothing were mapped by selected Computer-Aided Design (CAD) software. In the designed assembly models, different scales of the resolution were used for the particular layers – a homogenization for nonwoven fabrics model and designing the geometry of the individual yarns in the model of woven fabrics. Then, the finite volume method to simulate heat transfer through the assemblies caused by their exposure to the flame was applied. Finally, the simulation results with experimental measurements conducted according to the EN ISO 9151 were compared. Based on both the experimental and simulation results, parameters describing the tested clothing protective features directly affecting the firefighter’s safety were determined. As a result of the experiment and simulations, comparable values of these parameters were determined, which could show that used methods are an efficient tool in studying the thermal properties of multilayer protective clothing.

7

Experimental and numerical analysis of blood flow in roughness impact-R test

Kopernik Magdalena, Kruczek Dawid, Kurtyka Przemysław, Pomorska Małgorzata, Major Roman

Acta of Bioengineering and Biomechanics

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2022

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Vol. 24, no. 3

120--133

EN

The present paper covers simulation of blood flow in a roughness impact-R test model to anticipate the hemodynamic conditions of adhesion of blood elements to the modified surface. It was performed using numerical modelling of this process. The aim of these simulations was to create a surface morphology that stimulates the adhesion of blood elements to the surface of base plate of impact-R test. Methods: The morphology of base plate of impact-R test was developed using a vacuum powder sintering of commercial purity titanium powder (CP-Ti) on Ti6Al7Nb substrate. The finite volume method (FVM) and disperse particle method (DPM) were applied to develop the target model of a roughness impact-R test. The morphology of modified surfaces was documented with digital microscope and SEM (scanning electron microscopy). Results: The impact-R test developed using the two-phase blood model performed on regularly structured base plate resulted in shear stress values higher than the analogous for the model lacking such modification. The most significant reduction in maximum values of shear stress occurred in case of the DPM model and especially in the model with regular structures. Conclusions: The proposed models are very effective in modeling of the analysis of blood flow in roughness impact-R test.

8

Discrete phase model of blood flow in a roughness microchannel simulating the formation of pseudointima

Kopernik Magdalena, Dyrda Karina, Kurtyka Przemysław, Major Roman

Acta of Bioengineering and Biomechanics

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2022

|

Vol. 24, no. 1

132--144

EN

The goal of the present study was the development of discrete phase model to simulate the phenomenon of backfilling a morphologically complex surface by red blood cells (RBCs) in a flow microchannel and to anticipate the conditions of forming a pseudointima. The objective of the experimental studies that inspired the development of the simulation was to create a surface that stimulates the formation of the pseudointima layer. Methods: The finite volume method (FVM) and discrete particle method (DPM) were applied to develop the target model. In addition, a mixture model and a roughness model of bottom layer were tested in the present study to show their influence on simulation the phenomenon of backfilling a morphologically complex surface by RBCs in a flow microchannel. Results: Numerical models were developed including: a) FVM models to compare the effect of applying boundary conditions with/without roughness and cubes, as well as the analysis of their influence on blood velocity and shear stress; b) mixture models to compare the effect of applying different boundary conditions and cubes on computed results; c) DPM models to compare the effect of applying and not applying roughness as a boundary condition; d) DPM models with a morphologically complex surface and RBCs collisions to present RBCs concentration, velocity and time distributions during flow in a channel. Conclusions: The analysis carried out for the developed numerical models indicates that DPM model with cubes computes the best results. It also shows the backfilling of a morphologically complex surface of the bottom microchannel with RBCs.

9

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

Mostefai Mohamed Lamine, Choucha Abdelbaki, Cherif Bahri

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

510--526

EN

In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1 . Results of numerical experiments are presented to validate the theoretical analysis.

10

Numerical study of detonation processes in rotating detonation engine and its propulsive performance

Yi Tae-Hyeong, Lou Jing, Turangan Cary Kenny, Wolanski Piotr

Transactions on Aerospace Research

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2020

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Nr 3 (260)

30--48

EN

Numerical studies on detonation wave propagation in rotating detonation engine and its propulsive performance with one- and multi-step chemistries of a hydrogen-based mixture are presented. The computational codes were developed based on the three-dimensional Euler equations coupled with source terms that incorporate high-temperature chemical reactions. The governing equations were discretized using Roe scheme-based finite volume method for spatial terms and second-order Runge-Kutta method for temporal terms. One-dimensional detonation simulations with one- and multi-step chemistries of a hydrogen-air mixture were performed to verify the computational codes and chemical mechanisms. In two-dimensional simulations, detonation waves rotating in a rectangular chamber were investigated to understand its flowfield characteristics, where the detailed flowfield structure observed in the experiments was successfully captured. Three-dimensional simulations of two-waved rotating detonation engine with an annular chamber were performed to evaluate its propulsive performance in the form of thrust and specific impulse. It was shown that rotating detonation engine produced constant thrust after the flowfield in the chamber was stabilized, which is a major difference from pulse detonation engine that generates repetitive and intermittent thrust.

PL

Przedstawiono badania numeryczne propagacji fali detonacyjnej w wirującym silniku detonacyjnym oraz jego wydajności pędnej z jedno- i wielostopniową mieszanką chemiczną na bazie wodoru. Kody obliczeniowe opracowano w oparciu o trójwymiarowe równania Eulera w połączeniu z pojęciami źródłowymi, które obejmują wysokotemperaturowe reakcje chemiczne. Obowiązujące równania zostały zdyskredytowane przy użyciu metody skończonej objętości opartej na schemacie Roe'a dla terminów przestrzennych oraz metody Runge-Kutta drugiego rzędu dla terminów czasowych. W celu weryfikacji kodów obliczeniowych i mechanizmów chemicznych przeprowadzono jednowymiarowe symulacje detonacji z jedno- i wieloetapowymi chemikaliami mieszaniny wodoru i powietrza. W symulacjach dwuwymiarowych badano fale detonacyjne obracające się w komorze prostokątnej w celu zrozumienia jej charakterystyki pola przepływu, gdzie udało się uchwycić szczegółową strukturę pola przepływu zaobserwowaną w doświadczeniach. Przeprowadzono trójwymiarowe symulacje dwufalowego wirującego silnika detonacyjnego z komorą pierścieniową w celu oceny jego właściwości pędnych w postaci ciągu i impulsu właściwego. Wykazano, że wirujący silnik detonujący wytwarza stały ciąg po ustabilizowaniu się pola przepływu w komorze, co stanowi istotną różnicę w stosunku do silnika detonującego impulsowo, który wytwarza powtarzalny i przerywany ciąg.

11

Numerical investigation on the effects of obstruction and side ratio on non-Newtonian fluid flow behavior around a rectangular barrier

Noferesti Sara, Ghassemi Hassan, Nowruzi Hashem

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 1

53--67

EN

In this paper, the characteristics of the flow and forced heat transfer of power law non-Newtonian fluids that flow around a quadrilateral and rectangular cylinder that are located in a 2D channel are investigated by use of the finite volume method (FVM) in a steady state flow regime. To this accomplishment, in the constant temperature, the effects of a different obstruction ratio, aspect ratio and Reynolds number are investigated. The Reynolds number in the range 5 ≤ Re ≤ 40, the power index in the range 0.5 ≤ n ≤ 1.4, the aspect ratio in the range 0.5 ≤ a ≤ 2, and the obstruction ratio in the range 0.125 ≤ b ≤ 0.5 were selected. By surveying the drag coefficient profiles, it’s concluded that as the obstruction ratio increases, the drag coefficient is increased, while an increase in the Reynolds number causes the lower drag coefficient. In addition, the drag coefficient is strongly increased by aspect ratio enhancements.

12

Numerical analysis of turbulent flow around twodimensional bodies using non-orthogonal body-fitted mesh

Tarafder M. Shahjada, Mursaline M. Al

International Journal of Applied Mechanics and Engineering

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2019

|

Vol. 24, no. 2

387--410

EN

This paper deals with the numerical simulation of a turbulent flow around two-dimensional bodies by the finite volume method with non-orthogonal body-fitted grid. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of scalar and vector variables. Turbulence is modeled by the turbulence model and wall functions are used to bridge the solution variables at the near wall cells and the corresponding quantities on the wall. A simplified pressure correction equation is derived and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The numerical procedure is validated by comparing the computed pressure distribution on the surface of NACA 0012 and NACA 4412 hydrofoils for different angles of attack with experimental data. The grid dependency of the solution is studied by varying the number of cells of the C-type structured mesh. The computed lift coefficients of NACA 4412 hydrofoil at different angles of attack are also compared with experimental results to further substantiate the validity of the proposed methodology.

13

Wpływ parametrów modelu na dokładność wyników symulacji przepływomierza

Jurkowski Sławomir, Janisz Karina

Autobusy : technika, eksploatacja, systemy transportowe

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2019

|

R. 20, nr 12

135--139

PL

W artykule przedstawiono analizę wpływu parametrów symulacji przepływu czynnika ściśliwego przez zwężkę Venturiego na dokładność uzyskiwanych rezultatów, z wykorzystaniem programu Ansys 2019 R2. Analiza została przeprowadzona w oparciu o wzorzec za jaki uznano wyniki obliczeń przepływu wg. normy PN-EN ISO 51674:2005. Rozważono wpływ modelu gazu i modelu turbulencji. Symulacji podlegała całość układu pomiarowego włącznie z przewodami impulsowymi.

EN

The article presents the analysis of the impact of the compressor flow simulation parameters through the Venturi tube on the accuracy of the obtained results. The Ansys 2019 R2 program was used for analysis. The analysis was carried out on the basis of the pattern for which the results of flow calculations according to standards PN-EN ISO 5167-4: 2005. The influence of the gas model and turbulence model was considered. The entire measurement system, including impulse lines, was subject to simulation.

14

Symulacja prostego silnika magnetohydrodynamicznego

Lipiński Sz., Supińska D.

Maszyny Elektryczne : zeszyty problemowe

|

2018

|

Nr 3 (119)

65--69

PL

Silnik magnetohydrodynamiczny jest maszyną elektryczną, w której elementem bezpośrednio wprawianym w ruch jest płyn znajdujący się w polu magnetycznym. W opisanym przykładzie taką rolę pełni osolona woda przewodząca prąd znajdująca się w zewnętrznym polu magnetycznym pochodzącym od magnesu ferrytowego. W artykule zawarto model matematyczny zjawisk pozwalający na przewidywanie zachowania się płynu oraz wykorzystany model numeryczny, który wstępnie zweryfikowano na modelu fizycznym w laboratorium. Omawiane urządzenie wprawia w ruch obrotowy wodę znajdującą się w szalce Petriego, której zewnętrzna ścianka wyłożona jest taśmą miedzianą. Na dnie szalki położony jest magnes ferrytowy w kształcie pierścienia. Całość zasilana jest prądem stałym przepływającym poprzez płyn z umieszczonej centralnie elektrody wykonanej z miedzianego drutu do znajdującej się na zewnątrz elektrody utworzonej z taśmy miedzianej, którą wyłożona jest zewnętrzna ścianka.

EN

Magnetohydrodynamic drive is a type of electric drive, where force acts directly on fluid without mechanical moving parts. The fluid in most cases conducts electric current in magnetic field creating force. Article includes mathematical model allowing to predict fluid behavior together with incorporated numerical model, which was preliminary verified on physical model on test rig. In described example salty water conducts direct current from central electrode made of copper wire to external electrode made of thin copper sheet covering external wall of Petri dish. External magnetic field is provided by ferrite magnet located on the bottom of the vessel. In result water spins in directions according to forces created in conductor exposed to magnetic field.

15

Stabilność rozwiązania zagadnienia brzegowego niestacjonarnego profilu temperatury w przegrodzie budowlanej

Owczarek M., Radzikowska-Juś W.

Inżynieria Bezpieczeństwa Obiektów Antropogenicznych

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2018

|

Nr 3-4

30--34

PL

Jedną z uniwersalnych a zarazem prostych metod dla numerycznego rozwiązywania zadań nieustalonego przewodzenia ciepła w obudowie budynku jest metoda objętości skończonych. Jednak, przy sformułowaniu jawnym konieczne jest dobranie kroku czasowego, gwarantującego stabilność rozwiązania. W tym artykule wartość takiego kroku czasowego została określona z warunku zerowej różnicy pomiędzy teoretycznym a numerycznym rozwiązaniem dla danej geometrii ściany. Rozpatrzono wpływ współczynnika przewodzenia ciepła ściany na długość kroku. Warunki brzegowe przyjęte w artykule odpowiadały obciążeniom ogniowym ściany schronu.

EN

One of the most simple and versatile method for numeric solving of the problems of transient heat conduction in the building envelope is the finite volume method. In explicit scheme however there is a problem of assuming correct time step for solution stability. In this article stable step value was determined from the condition of zero difference between the theoretical and numerical solution for the particular geometry of the wall. The influence of the thermal conductivity on the step length has been evaluated. Condition for the correctness of solutions obtained from the analysis in this article is sharper than the condition of equations stability according to the literature. For the boundary conditions adopted solution can be applied to the study of resistance of buildings shelters to long fire.

16

Modeling of Air Permeability of Knitted Fabric Using the Computational Fluid Dynamics

Puszkarz A. K., Krucińska I.

Autex Research Journal

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2018

|

Vol. 18, no. 4

364--376

EN

This article concerns the widespread matter of biophysical comfort. In this work, 10 double-layer knitted fabrics with potential application in multilayer garments addressed to a specific group of users, such as newborns, were investigated. The materials were constructed with the following raw materials: cotton, polypropylene, polyester, polyamide, bamboo, and viscose. The textiles with a comparable geometrical structure and different composition were tested for their air permeability. In the experimental part, the materials were tested in specific constant ambient conditions using an air permeability tester. In the simulation part, 3D models of actual textiles were designed and air permeability based on the performed simulations using finite volume method was calculated. Both measurements and simulations yielded comparable results and showed that the air permeability of the knitted fabric strongly depends on the thickness and geometrical parameters of yarn.

17

Numerical solutions of a steady 2-D incompressible flow in a rectangular domain with wall slip boundary conditions using the finite volume method

Ambethkar V., Srivastava M. K.

Journal of Applied Mathematics and Computational Mechanics

|

2017

|

Vol. 16, nr 2

5--16

EN

In this study, a finite volume method (FVM) is suitably used for solving the problem of a fully coupled fluid flow in a rectangular domain with slip boundary conditions. Numerical solutions for the flow variables, viz. velocity, and pressure have been computed. The FVM, with an upwind scheme, has been implemented to discretize the governing equations of the present problem. The well known SIMPLE algorithm is employed for pressure-velocity coupling. This was executed with the aid of a computer program developed and run in a C-compiler. Computations have been performed for unknown variables with Reynolds numbers (Re) = 50, 100, 250, 500, 750 and 1000. The behavior of steady-state solutions of velocity and pressure of the fluid along horizontal and vertical through geometric center of the rectangular domain have been illustrated. We observed that, with the increase of the Reynolds number, the absolute value of velocity components decreases whereas the pressure value increases.

18

Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

Yan J. L., Zheng L. H.

International Journal of Applied Mathematics and Computer Science

|

2017

|

Vol. 27, no. 3

515--525

EN

The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg–de Vries equation.

19

The geometric model-based patient-specific simulations of turbulent aortic valve flows

Stupak E., Kačianauskas R., Kačeniauskas A., Starikovičius V., Maknickas A., Pacevič R., Staškūnienė M., Davidavičius G., Aidietis A.

Archives of Mechanics

|

2017

|

Vol. 69, nr 4-5

317--345

EN

This paper presents the patient-specific simulations of the aortic valve based on the proposed geometric model. A structural analysis is performed by using the finite element method to determine the stress-strain state of the aortic valve. The study is focused on the investigation of various turbulence models crucial for the appropriate description of the flow in the deceleration phase, following the peak systole. A comparative study of the flow solution without a turbulence model and the numerical results obtained by using various turbulence models is also performed. The results yielded by the shear-stress transport k-ω model supplemented with the intermittency transition equation most closely match those of numerical simulations without a turbulence model.

20

Estimating rapid flow transients using extended Kalman filter

Uilhoorn F. E.

Silesian Journal of Pure and Applied Mathematics

|

2016

|

Vol. 6, iss. 1

97--110

EN

Theoretical and numerical modeling of ﬂow transients in pipelines is a challenging ﬁeld of research. The governing ﬂow equations constitute a system of nonlinear hyperbolic partial diﬀerential equations enforcing the conservation laws for mass, momentum and energy. The application of these mathematical models might be limited due to the absence of complete knowledge about the physical phenomena and uncertainties. Information about the initial and boundary conditions is usually obtained from measurements. The presence of noise and inaccuracies, as well as inexactness of the ﬂow model and numerical approximations for solving the full model can lead to predictions that diﬀer from reality. In this paper, we deal with the problem of extracting information about states of the system in real time given noisy measurements. We solved the isothermal ﬂow model during a hydraulic shock while using the extended Kalman ﬁlter to estimate the hidden state variables. To avoid spurious oscillations in the solution, the ﬂow model in conservative form was solved using Roe’s ﬂux limiter within the ﬁnite volume framework to ensure the total variation diminishing property. Numerical approximation of the Jacobian was done with an adaptive routine and showed that most entries in the matrix are zero and therefore sparse. The robustness of the extended Kalman ﬁlter was examined by varying the noise statistics. In most of the situations, we can conclude that the extended Kalman ﬁlter was successful in estimating the rapid transients of natural gas.