Hydraulic piston accumulators play a major role especially within the field of stationary hydraulics. The calculation of the amount of hydraulic energy which can be stored in such an accumulator is crucial when it comes to a precise system design. The knowledge of the temperature and pressure within the accumulator is required in order to calculate the amount of energy to be stored. The state of the art solution to estimate the state of change of such an accumulator is the implementation of a costly measurement system within the accumulator which tracks the position of the piston. The goal of this paper is to develop and to analyse a time efficient simulation approach for the gaseous phase within a piston accumulator depending on the accumulator’s load cycle. Temperature, pressure, density and velocity profiles inside of the gaseous phase are calculated transiently in order to achieve that goal. The simulation model is derived in one dimensional environment to save computational effort. Having derived a valid model of the gaseous phase it will be possible in future works to replace the expensive position measurement system by pressure and temperature transducers and then use the model to calculate the position of the piston and therefore estimate the state of change.

<p>Karakteristika hiperboličnih sistema zakona odrržanja je da čak i u slučaju glatkog po-četnog uslova re&scaron;enja uglavnom razvijaju prekide u konačnom vremena. Zbog toga se posmatraju slaba re&scaron;enja koja dati sistem zadovoljavaju u distributivnom smislu i mogu biti čak i neograničena &scaron;to se ispoljava kroz pojavu Dirakove delta funkcije u re&scaron;enju. U ovoj disertaciji se akcenat stavlja na analizu protoka sti&scaron;ljivog neviskoznog fluida koji ne menja pravac prilikom kretanja. Protok je opisan Ojlerovim sistemom iz gasne dinamike koji se sastoji iz zakona održanja mase, količine kretanja i energije, dok su karakteristike fluida određene konstitutivnim relacijama. U slučaju izentropskog ili izotermnog protoka sistem se svodi na zakone održanja mase i količine kretanja. Glatka re&scaron;enja takvog sistema automatski zadovoljavaju zakon održanja energije, dok prelaskom na slabu formulaciju dolazi do gubitka energije. Za predstavnike sistema gasne dinamike sa nepozitivnim pritiskom su uzeti sistem gasne dinamike bez pritiska i model za&nbsp; Čapliginov gas i njegova uop&scaron;tenja. Data su re&scaron;enja Rimanovih problema za te sisteme koja se mogu predstaviti kao kombinacija klasičnih elementarnih talasa i senka talasa koji aproksimiraju re&scaron;enja u obliku delta udarnih talasa i koji omogućavaju re&scaron;avanje početnog problema koji u početnom uslovu sadrži delta funkciju. Na primeru modela za uop&scaron;ten Čapliginov gas dokazano je da uslov prekompresivnosti nije jači od entropijskog uslova, &scaron;to je prvi takav rezultat u literaturi. Dalje su kori&scaron;ćena re&scaron;enja Rimanovih problema, kao i problema singularne interakcije i dat je algoritam za konstrukciju globalnog dopustivog približnog re&scaron;enja početnog problema za sistem gasne dinamike bez pritiska. Algoritam je univerzalan i ideja se može pro&scaron;iriti na veliki broj sistema zakona održanja i veliki broj početnih uslova. Diskutovane su promene energije u približnom re&scaron;enju i posle interakcija. Dobijeno približno re&scaron;enje slabo konvergira u prostoru Radonovih mera sa predznakom.</p> / <p>&nbsp;</p><p class="MsoNormal">A solutions to hyperbolic conservation laws systems starting out as smooth often develop singularities in a finite time. As a consequence, we are forced to look for weak solutions that satisfy the system in distributional sense. Those solutions are often unbounded, which is expressed through the appearance of Dirac delta function. In this theses we study a one-dimensional, compressible and inviscid flow of a fluid. The process is described by compressible Euler gas dynamics system which consists of conservation laws of mass, linear momentum and energy, while the characteristics of the fluid are described using constitutive relations. In the case of isentropic or isothermal flow the system reduces to conservation laws of mass and linear momentum. The energy is conserved for smooth solutions to such systems, but while passing to the weak formulation the energy is being dissipated. As representatives, we&nbsp; consider pressureless gas dynamics system, as well as Chaplygin gas model and its generalizations. We give the solutions to Riemann problems which can be represented as a combinations of classical elementary waves and shadow waves that approximate the solutions in the form of delta shock and allow as to solve the problems with initial data containing delta function. We use generalized Chaplygin gas model as demonstration of the fact that overcompressibility condition is not stronger that entropy condition, which is the first result of that kind in the literature. Further, we use solutions&nbsp; to the Riemann problems, as well as singular interaction problems to give the algorithm for construction of global admissible approximate solution to the pressureless gas dynamics initial value problem. The algorithm is universal and idea can be applied to large number of conservation laws systems and large number of initial data. We discuss&nbsp; energy changes in approximate solution and after the interactions. 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Des percées récentes ont été faites dans l’étude des trous noirs supermassifs (SMBH), grâce en grande partie à l’équipe du télescope de l’horizon des évènements (EHT). Cependant, déterminer la masse de ces entités colossales à des décalages vers le rouge élevés reste un défi de taille pour les astronomes. Il existe diverses méthodes directes et indirectes pour mesurer la masse de SMBHs. La méthode directe la plus précise consiste à résoudre la cinématique du gaz moléculaire, un traceur froid, dans la sphère d’influence (SOI) du SMBH. La SOI est définie comme la région où le potentiel gravitationnel du SMBH domine sur celui de la galaxie hôte. Par contre, puisque la masse d’un SMBH est négligeable face à la masse d’une galaxie, la SOI est, d’un point de vue astronomique, très petite, typiquement de quelques dizaines de parsecs. Par conséquent, il faut une très haute résolution spatiale pour étudier la SOI d’un SMBH et pouvoir adéquatement mesurer sa masse. C’est cette nécessité d’une haute résolution spatiale qui limite la mesure de masse de SMBHs à de plus grandes distances. Pour briser cette barrière, il nous faut donc trouver une manière d’améliorer la résolution spatiale d’objets observés à un plus au décalage vers le rouge. Le phénomène des lentilles gravitationnelles fortes survient lorsqu’une source lumineuse en arrière-plan se trouve alignée avec un objet massif en avant-plan, le long de la ligne de visée d’un observateur. Cette disposition a pour conséquence de distordre l’image observée de la source en arrière-plan. Puisque cette distorsion est inconnue et non-linéaire, l’analyse de la source devient nettement plus complexe. Cependant, ce phénomène a également pour effet d’étirer, d’agrandir et d’amplifier l’image de la source, permettant ainsi de reconstituer la source avec une résolution spatiale considérablement améliorée, compte tenu de sa distance initiale par rapport à l’observateur. L’objectif de ce projet consiste à développer une chaîne de simulations visant à étudier la faisabilité de la mesure de la masse d’un trou noir supermassif (SMBH) par cinéma- tique du gaz moléculaire à un décalage vers le rouge plus élevé, en utilisant l’apprentissage automatique pour tirer parti du grossissement généré par la distorsion d’une forte lentille gravitationnelle. Pour ce faire, nous générons de manière réaliste des observations du gaz moléculaire obtenues par le Grand Réseau d’Antennes Millimétrique/Submillimétrique de l’Atacama (ALMA). Ces données sont produites à partir de la suite de simulations hydrody- namiques Rétroaction dans des Environnements Réalistes (FIRE). Dans chaque simulation, l’effet cinématique du SMBH est intégré, en supposant le gaz moléculaire virialisé. Ensuite, le flux d’émission du gaz moléculaire est calculé en fonction de sa vitesse, température, densité, fraction de H2, décalage vers le rouge et taille dans le ciel. Le cube ALMA est généré en tenant compte de la résolution spatiale et spectrale, qui dépendent du nombre d’antennes, de leur configuration et du temps d’exposition. Finalement, l’effet de la forte lentille gravi- tationnelle est introduit par la rétro-propagation du faisceau lumineux en fonction du profil de masse de l’ellipsoïde isotherme singulière (SIE). L’exploitation de ces données ALMA simulées est testée dans le cadre d’un problème de régression directe. Nous entraînons un réseau de neurones à convolution (CNN) à apprendre à prédire la masse d’un SMBH à partir des données simulées, sans prendre en compte l’effet de la lentille. Le réseau prédit la masse du SMBH ainsi que son incertitude, en supposant une distribution a posteriori gaussienne. Les résultats sont convaincants : plus la masse du SMBH est grande, plus la prédiction du réseau est précise et exacte. Tout comme avec les méthodes conventionnelles, le réseau est uniquement capable de prédire la masse du SMBH tant que la résolution spatiale des données permet de résoudre la SOI. De plus, les cartes de saillance du réseau confirment que celui-ci utilise l’information contenue dans la SOI pour prédire la masse du SMBH. Dans les travaux à venir, l’effet des lentilles gravitationnelles fortes sera introduit dans les données pour évaluer s’il devient possible de mesurer la masse de ces mêmes SMBHs, mais à un décalage vers le rouge plus élevé. / Recent breakthroughs have been made in the study of supermassive black holes (SMBHs), thanks largely to the Event Horizon Telescope (EHT) team. However, determining the mass of these colossal entities at high redshifts remains a major challenge for astronomers. There are various direct and indirect methods for measuring the mass of SMBHs. The most accurate direct method involves resolving the kinematics of the molecular gas, a cold tracer, in the SMBH’s sphere of influence (SOI). The SOI is defined as the region where the gravitational potential of the SMBH dominates that of the host galaxy. However, since the mass of a SMBH is negligible compared to the mass of a galaxy, the SOI is, from an astronomical point of view, very small, typically a few tens of parsecs. As a result, very high spatial resolution is required to study the SOI of a SMBH and adequately measure its mass. It is this need for high spatial resolution that limits mass measurements of SMBHs at larger distances. To break this barrier, we need to find a way to improve the spatial resolution of objects observed at higher redshifts. The phenomenon of strong gravitational lensing occurs when a light source in the back- ground is aligned with a massive object in the foreground, along an observer’s line of sight. This arrangement distorts the observed image of the background source. Since this distor- tion is unknown and non-linear, analysis of the source becomes considerably more complex. However, this phenomenon also has the effect of stretching, enlarging and amplifying the image of the source, enabling the source to be reconstructed with considerably improved spatial resolution, given its initial distance from the observer. The aim of this project is to develop a chain of simulations to study the feasibility of measuring the mass of a supermassive black hole (SMBH) by kinematics of molecular gas at higher redshift, using machine learning to take advantage of the magnification generated by the distortion of a strong gravitational lens. To this end, we realistically generate observations of molecular gas obtained by the Atacama Large Millimeter/Submillimeter Antenna Array (ALMA). These data are generated from the Feedback in Realistic Environments (FIRE) suite of hydrodynamic simulations. In each simulation, the kinematic effect of the SMBH is integrated, assuming virialized molecular gas. Next, the emission flux of the molecular gas is calculated as a function of its velocity, temperature, density, H2 fraction, redshift and sky size. The ALMA cube is generated taking into account spatial and spectral resolution, which depend on the number of antennas, their configuration and exposure time. Finally, the effect of strong gravitational lensing is introduced by back-propagating the light beam according to the mass profile of the singular isothermal ellipsoid (SIE). The exploitation of these simulated ALMA data is tested in a direct regression problem. We train a convolution neural network (CNN) to learn to predict the mass of an SMBH from the simulated data, without taking into account the effect of the lens. The network predicts the mass of the SMBH as well as its uncertainty, assuming a Gaussian a posteriori distribution. The results are convincing: the greater the mass of the SMBH, the more precise and accurate the network’s prediction. As with conventional methods, the network is only able to predict the mass of the SMBH as long as the spatial resolution of the data allows the SOI to be resolved. Furthermore, the network’s saliency maps confirm that it uses the information contained in the SOI to predict the mass of the SMBH. In future work, the effect of strong gravitational lensing will be introduced into the data to assess whether it becomes possible to measure the mass of these same SMBHs, but at a higher redshift.

The numerics of hyperbolic conservation laws, e.g., the Euler equations of gas dynamics, shallow water equations and MHD equations, is non-trivial due to the convective terms being highly non-linear and equations being coupled. Many numerical methods have been developed to solve these equations, out of which central schemes and upwind schemes (such as Flux Vector Splitting methods, Riemann solvers, Kinetic Theory based Schemes, Relaxation Schemes etc.) are well known. The majority of the above mentioned schemes give rise to very dissipative solutions. In this thesis, we propose novel low dissipative numerical algorithms for some hyperbolic conservation laws representing fluid flows. Four different and independent numerical methods which give low diffusive solutions are developed and demonstrated. The first idea is to regulate the numerical diffusion in the existing dissipative schemes so that the smearing of solution is reduced. A diffusion regulator model is developed and used along with the existing methods, resulting in crisper shock solutions at almost no added computational cost. The diffusion regulator is a function of jump in Mach number across the interface of the finite volume and the average Mach number across the surface. The introduction of the diffusion regulator makes the diffusive parent schemes to be very accurate and the steady contact discontinuities are captured exactly. The model is demonstrated in improving the diffusive Local Lax-Friedrichs (LLF) (or Rusanov) method and a Kinetic Scheme. Even when employed together with accurate methods of Roe and Osher, improvement in solutions is demonstrated for multidimensional problems. The second method, a Central Upwind-Biased Scheme (CUBS), attempts to reorganize a central scheme such that information from irrelevant directions is largely reduced and the upwind biased information is retained. The diffusion co-efficient follows a new format unlike the use of maximum characteristic speed in the Local Lax-Friedrichs method and the scheme results in improved solutions of the flow features. The grid-aligned steady contacts are captured exactly with the reorganized format of diffusion co-efficient. The stability and positivity of the scheme are discussed and the procedure is demonstrated for its ability to capture all the features of solution for different flow problems. Another method proposed in this thesis, a Central Rankine-Hugoniot Solver, attempts to integrate more physics into the discretization procedure by enforcing a simplified Rankine-Hugoniot condition which describes the jumps and hence resolves steady discontinuities very accurately. Three different variants of the scheme, termed as the Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), based on a single wave (MOVERS-1), multiple waves (MOVERS-n) and limiter based diffusion (MOVERS-L) are presented. The scheme is demonstrated for scalar Burgers equation and systems of conservation laws like Euler equations, ideal Magneto-hydrodynamics equations and shallow water equations. The new scheme uniformly improves the solutions of the Local Lax-Friedrichs scheme on which it is based and captures steady discontinuities either exactly or very accurately. A Grid-Free Central Solver, which does not require a grid structure but operates on any random distribution of points, is presented. The grid-free scheme is generic in discretization of spatial derivatives with the location of the mid-point between a point and its neighbor being used to define a relevant coefficient of numerical dissipation. A new central scheme based on convective-pressure splitting to solve for mid-point flux is proposed and many test problems are solved effectively. The Rankine-Hugoniot Solver, which is developed in this thesis, is also implemented in the grid-free framework and its utility is demonstrated. The numerical methods presented are solved in a finite volume framework, except for the Grid-Free Central Solver which is a generalized finite difference method. The algorithms developed are tested on problems represented by different systems of equations and for a wide variety of flow features. The methods presented in this thesis do not need any eigen-structure and complicated flux splittings, but can still capture discontinuities very accurately (sometimes exactly, when aligned with the grid lines), yielding low dissipative solutions. The thesis ends with a highlight on the importance of developing genuinely multidimensional schemes to obtain accurate solutions for multidimensional flows. The requirement of simpler discretization framework for such schemes is emphasized in order to match the efficacy of the popular dimensional splitting schemes.

Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work. / Graduate

The role of clusters in planetary atmospheres and the interstellar medium is potentially important. Investigating such a role requires basic experimental information, however lacking. The goal of this thesis was to develop an efficient experimental set-up to produce clusters in the laboratory in concentrations large enough to allow their high resolution spectra to be recorded, thus providing the necessary data allowing the physico-chemical properties of the clusters to be studied.<p>The study of this subject however suffers from the lack of basic experimental data. The goal is therefore to produce clusters in the laboratory in concentration large enough to record their high resolution spectrum. This is the initial aim of the present thesis.<p>During this work, we have built and extensively tested a new experimental set-up called FANTASIO (``Fourier trANsform, Tunable diode and quadrupole mAss spectrometers interfaced to a Supersonic expansIOn'). With the help of this new device, various experiments on jet-cooled species have been performed.<p>The cartography of the supersonic expansion was established, using the mass spectrometer as a moving pressure probe. This enabled us to characterize the geometrical properties of the supersonic jet produced by circular and slit nozzles and to determine the position of the virtual nozzle. The effect of the axisymmetric expansion geometry on the R(0) lineshape in the nu_3 band of N_2O, recorded by FTIR, was also investigated.<p>The rotational temperature of the jet-cooled molecules was determined to be a few K by measuring the intensity of lines in spectra recorded by FTIR spectroscopy.<p>Vibrational energy transfer occuring in the expansion between N_2O molecules and different collision partners was investigated on the nu_2+nu_3-nu_2 band of N_2O, again using FTIR spectroscopy. The trend of these transfers was found to be related to the energy difference between the v_2=1 level of N_2O and the closest vibrational state in the collision partner, with the largest population.<p>The sensitivity of the set-up was enhanced by a factor of 5 by increasing the absorption path length, using a multipass system. A procedure to remove the residual gas contribution from the IR spectra was developped, based on the mass spectrometer. Thanks to this sensitivity increase, broadband absorption features of clusters were observed for a C_2H_2-Ar mixture in circular and slit expansions.<p>The optical sensitivity of FANTASIO was again increased by the implementation of the CW-CRDS system. The enhancement over FTIR was calculated to be over a factor 750. Thanks to this drastic improvement, spectral signatures of various clusters were recorded, such as C_2H_2-Ar, C_2H_2 multimers, C_2H_2-N_2O and C_2H_2-CO_2, at high resolution.<p>The role of clustering in generating unusual line shapes of acetylene in an axisymmetric expansion was investigated. We demonstrated that C_2H_2 aggregates produced in the expansion are responsible for central dips observed in the monomer absorption. These acetylene clusters thus appear to be formed in the centre of the expansion, while, unexpectedly, acetylene-Ar complexes are formed at the edge of the conical expansion.<p>Various research prospects were explored during this thesis thanks to the FANTASIO device, opening new research directions. FANTASIO is today operational and defines a useful tool to achieve the study of small clusters by infrared spectroscopy./<p><p>Le rôle des agrégats dans les atmosphères planétaires et dans le milieu interstellaire est potentiellement important. Cependant, les études sur ce sujet souffrent du manque de données expérimentales. Le but de cette thèse était de développer un dispositif expérimental efficace pour produire au laboratoire des agrégats en quantité suffisante pour permettre l'enregistrement de leur spectre infrarouge à haute résolution et donc l'étude de leurs propriétés physico-chimiques.<p>Durant ce travail, nous avons construit et testé un nouveau dispositif expérimental appelé FANTASIO, basé sur un jet supersonique couplé à un spectromètre de masse, un spectromètre à transformée de Fourier et un système CRDS. Grâce à cet appareillage, différentes expériences sur des molécules à basse température ont été menées.<p>L'expansion supersonique a été cartographiée en utilisant le spectromètre de masse comme une sonde de pression mobile. Cette cartographie nous a permis d'établir les propriétés géométriques des jets supersoniques produits par les orifices circulaire et de type fente, et de déterminer la position de l'orifice virtuel. L'effet de la géométrie de l'expansion sphérique sur le profil de la raie R(0) de la bande nu_3 de N_2O, enregistré par FTIR, a aussi été étudié.<p>Une température rotationnelle de quelques K a été déterminée pour les molécules refroidies en jet supersonique par mesure de la distribution d'intensité de raies dans les spectres enregistrés par FTIR.<p>Le transfert d'énergie vibrationnelle entre des molécules de N_2O et différents partenaires collisionnels a été étudié en analysant l'intensité de la bande nu_2+nu_3-nu_2 de N_2O, enregistré également par spectroscopie FTIR. Il a été trouvé que la tendance de ces transferts est liée à la différence d'énergie entre le niveau v_2=1 de N_2O et l'état vibrationnel le plus proche et le plus peuplé du partenaire collisionnel.<p>La sensibilité du dispositif a été augmentée d'un facteur 5 dû à l'allongement du chemin d'absorption, grâce à l'utilisation d'un système multipassage. Une procédure basée sur l'utilisation du spectromètre de masse et visant à enlever la contribution du gaz chaud résiduel dans les spectres infrarouges a été mise au point. Grâce à cette augmentation de sensibilité, des structures d'absorption non résolues d'agrégats ont été observées dans des expansions en trou et en fente d'un mélange de C_2H_2-Ar.<p>La sensibilité optique de FANTASIO a encore été augmentée par l'ajout au dispositif d'un système CW-CRDS. L'amélioration par rapport au spectromètre à transformée de Fourier a été calculée comme étant supérieure à un facteur 750. Grâce à cette importante amélioration, les signatures spectrales de divers agrégats, tels que C_2H_2-Ar, des multimères de C_2H_2, C_2H_2-N_2O et C_2H_2-CO_2, ont été enregistrées à haute résolution.<p>Le rôle de l'agrégation dans la génération de profils de raie inhabituels dans une expansion en trou de l'acétylène a été étudié. Nous avons démontré que les agrégats de C_2H_2 produits dans le jet supersonique sont responsables des creux observés dans le profil d'absorption du monomère. Ces agrégats apparaissent donc comme étant formés au centre de l'expansion, tandis que, de manière inattendue, les agrégats de C_2H_2-Ar sont formés aux bords de l'expansion conique.<p>Plusieurs idées de recherche ont été explorées durant cette thèse grâce au dispositif FANTASIO, ouvrant de nouvelles directions de recherche. FANTASIO est aujourd'hui opérationnel et se présente comme un outil utile dans l'étude des petits agrégats par spectroscopie infrarouge. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.