3,759 research outputs found

    Quantum algorithm for smoothed particle hydrodynamics

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    We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers

    A second order directional split exponential integrator for systems of advection–diffusion–reaction equations

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    We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection–diffusion–reaction equations in two and three space dimensions. It is based on a directional splitting of the involved matrix functions, which allows for a simple yet efficient implementation through the computation of small sized exponential-like functions and tensor-matrix products. The procedure straightforwardly extends to the case of an arbitrary number of components and to any space dimension. Several numerical examples in 2D and 3D with physically relevant (advective) Schnakenberg, FitzHugh–Nagumo, DIB, and advective Brusselator models clearly show the advantage of the approach against state-of-the-art techniques

    Jets and instabilities in forced magnetohydrodynamic flows

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    Magnetic fields are present in the solar system and astrophysical bodies (e.g. the Sun's field, the Earth's field, and the fields of giant planets, stars and galaxies). Our research examines the effect of magnetic fields on these systems, extending the work of Meshalkin and Sinai (1961) & Manfroi and Young (2002). The results will be useful for understanding the effects of the magnetic field in more turbulent regimes, although this study is concerned with the instabilities associated with classical laminar flow. We aim to investigate the role played by the magnetic field in modifying the stability properties of planar-forced fluid flows. In the absence of magnetic fields, the flow found by a body force, and nonlinear interactions with Rossby waves result in the generation of strong zonal flows. However, we find that the presence of a weak magnetic field suppresses the zonal jet generation. Here we study the instabilities of the Kolmogorov flow. We consider u_0=(0,sin x ) as a 2D incompressible flow. In the presence of a mean magnetic field, the dynamics are governed by the Navier–Stokes equations and the induction equation. We perform a classical linear analysis, in which growth rate, stability criteria, and MHD effects are derived. Instabilities are investigated associated with two magnetic field orientations, which can be x-directed (horizontal) or y-directed (vertical}) in our two-dimensional system to give an MHD version of Kolmogorov flow. In a basic equilibrium state magnetic field lines are straight for the case of vertical field and sinusoidal for horizontal field with an additional component of the external force balancing the resulting Lorentz force

    An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

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    We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3(134.2 million) finite elements run in less than 32 seconds per iteration with a peak memory of 21 GB. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d

    Wall Temperature and Leading-Edge Bluntness Effects in Hypersonic Laminar Separation

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    This thesis considers wall-temperature and leading-edge bluntness effects on hypersonic laminar separation, using both the interactive boundary layer theory and Computational Fluid Dynamics. Firstly, we studied the effect of wall temperature and leading-edge bluntness on hypersonic laminar separation induced by a finite-span compression corner. The flow conditions were: Mach number 9.66; Reynolds number 1.34 × 106 per metre; and stagnation temperature 3150 K. The wall-to-stagnation temperature ratio varied from 0.095 to 0.333. Two leading-edge bluntnesses of 40 μm and 200 μm were used in the investigation. Numerical solutions were obtained using a compressible Navier-Stokes solver, and compared with the triple-deck theory using the numerical method of Ruban (1978) and Cassel et al. (1995). Separation was induced by ramp angles of 10◦ and 20◦ , which produced incipient and large separations, respectively. The corresponding scale angles were not sufficient to induce secondary separation. Two regimes of shock intereference were identified depending on the wall temperature ratio. Increasing both the wall temperature ratio and blunting increased the separation length. The corner instability in the form of a stationary wave-packet identified by Cassel et al. (1995) for scale angles α ≥ 3.9 was investigated but was shown to be a numerical artefact of the algorithm rather than having any physical basis. We attempted to solve the steady-state triple-deck equations using the method of Bos & Ruban (2000) for supersonic flow past a compression corner. This was motivated by the fact that in their above paper they show solutions for scale angles up to 8, the highest obtained so far in the literature. However, we encountered a stationary wave-packet at the corner for scale angles 1.82 and 1.96, depending on the values of stretching factors. Our solutions are then compared with the steady-state solutions produced using the method of Logue et al. (2014), which do not show such wave-packets. These wave-packets do not appear to be the result of flow instability, as flow instabilities should only appear with unsteady equations (Cassel et al., 1995). It is therefore suggested that the method of Bos & Ruban (2000) produces these spurious wave-packets as a consequence of their numerical method. This has important implications in the interpretation of triple-deck solutions. We discuss a relationship between wave-packets and discontinuities encountered in the numerical solution of unsteady, supersonic triple-deck equations. Large gradients at the corner are found to compromise the stability of the algorithm of Cassel et al. (1995) as the scale angle increases. Two numerical methods have been developed to deal with such gradients. The first method is a time-splitting explicit method with a first-order approximation of the pressure derivative (FOM). This improves the stability of the algorithm at the cost of added numerical diffusion. The range of solutions obtained was extended from 3.7 by Cassel et al. (1995) to 6.5. The diffusivity of this method is quantified by comparing with the steady state solutions of Korolev et al. (2002) and Logue et al. (2014). The appearance of a spike just prior to the second minimum in shear stress also seen by some previous researchers is elucidated. The second method, which is new, is the Haar Wavelet Method (HWM) applied to unsteady triple-deck equations. This method is found to be stable and accurate, but computationally very expensive. Finally, our results are analysed in terms of the maximum pressure gradient prior to reattachment and the second shear stress minimum as defined and discussed in Smith & Khorrami (1991). Finally, we also considered an axisymmetric compression corner, using the interactive boundary layer theory. The problem of axisymmetric supersonic laminar separation over a compression corner has not been considered within the framework of triple-deck theory for several decades, despite significant advances in both theoretical methods and numerical techniques. We revisited the problem considered by Gittler & Kluwick (1987), using two numerical methods; the method of Ruban (1978) and Cassel et al. (1995), termed Ruban-Cassel Method (RCM); and the Haar Wavelet Method (HWM). The solution for both numerical methods shows good agreement for both shear-stress and pressure values. At a scale angle 6.8, the Ruban-Cassel Method produces a wave-packet similar to that encountered by Cassel et al. (1995). Using the Haar Wavelet Method, wave have been able to show results for scale angles up to 10 without encountering such a wave-packet. Incipient secondary separation is shown to occur for a scale angle of 10. Secondary separation was not observed by Gittler & Kluwick (1987) for scale angles as high as 9. It is suggested that this is possibly due to the Reyhner & Flügge-Lotz (1968) approximation used in their calculations, which neglects the convective term in the reverse flow

    Numerical resolution of the Navier-Stokes equations with parallel programming for the analysis of heat and mass transfer phenomena.

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    Aquesta tesi analitza mètodes numèrics per resoldre les equacions de Navier-Stokes en dinàmica de fluids computacional (CFD, per les sigles en anglès). La investigació es centra a des- envolupar una visió profunda de diferents mètodes numèrics i la seva aplicació a diversos fenòmens de transport. S’aplica una metodologia pas a pas, que abarca l’anàlisi de volums fi- nits i mètodes espectrals, la validació de models i la verificació de codis a través de l’anàlisi de casos d’estudi de convecció-difusió, flux de fluids i turbulència. La investigació revela l’efecte de diferents esquemes d’aproximació a la solució numèrica i emfatitza la importància d’una representació física precisa juntament amb la solidesa matemàtica. S’examina la convergència del mètode de resolució d’equacions iteratiu pel que fa a la naturalesa de la física de l’estudi, i cal destacar la necessitat de tècniques de relaxació apropiades. A més, s’explora el mètode de passos fraccionats per resoldre el fort acoblament de pressió-velocitat a les equacions de Navier-Stokes, mentre es considera l’addició d’altres fenòmens de transport. L’anàlisi de fluxes turbulents mostra la cascada d’energia a l’espai de Fourier i l’efecte del truncament a causa de la discretització espacial o espectral, abordat per l’aplicació de models simplificats, com ara Large Eddy Simulation (LES), aconseguint una solució aproximada amb un menor cost computacional. A més, s’analitza la implementació de la computació en paral·lel utilitzant l’estàndard MPI, emfatitzant-ne l’escalabilitat i el potencial per abordar les demandes creixents de l’anàlisi CFD en els camps de l’enginyeria. En general, aquesta recerca proporciona informació valuosa sobre els mètodes numèrics per a les equacions de Navier-Stokes, la seva aplicació a CFD i les implicacions pràctiques per als processos d’enginyeriaEsta tesis analiza métodos numéricos para resolver las ecuaciones de Navier-Stokes en dinámica de fluidos computacional (CFD, por sus siglas en Inglés). La investigación se centra en desarrollar una visión profunda de distintos métodos numéricos y su aplicación a diversos fenómenos de transporte. Se aplica una metodología paso a paso, que abarca el análisis de volúmenes finitos y métodos espectrales, validación de modelos y verificación de códigos a través del analisis de casos de estudio de convección-difusión, flujo de fluidos y turbulencia. La investigación revela el efecto de diferentes esquemas de aproximación en la solución numérica y enfatiza la importancia de una representación física precisa junto con la solidez matemática. Se examina la convergencia del método de resolución de equaciones iterativo con respecto a la naturaleza de la física del estudio, destacando la necesidad de técnicas de relajación apropiadas. Además, se explora el método de pasos fraccionados para resolver el fuerte acoplamiento de presión-velocidad en las ecuaciones de Navier-Stokes, mientras se considera la adición de otros fenómenos de transporte. El análisis de flujos turbulentos muestra la cascada de energía en el espacio de Fourier y el efecto del truncamiento debido a la discretización espacial o espectral, abordado por la aplicación de modelos simplificados, como Large Eddy Simulation (LES), logrando una solución aproximada con un menor costo computacional. Además, se analiza la implementación de la computación en paralelo utilizando el estándar MPI, enfatizando su escalabilidad y potencial para abordar las crecientes demandas del análisis CFD en los campos de la ingeniería. En general, esta investigación proporciona información valiosa sobre los métodos numéricos para las ecuaciones de Navier-Stokes, su aplicación a CFD y sus implicaciones prácticas para los procesos de ingenieríaThis thesis analyzes numerical methods for solving the Navier-Stokes equations in computational fluid dynamics (CFD). The research focuses on developing a deep insight into different numerical techniques and their application to various transport phenomena. A step-by-step methodology is applied, encompassing the analysis of finite volume and spectral methods, model validation, and code verification with the study of convection-diffusion, fluid flow, and turbulence study cases. The investigation reveals the effect of different approximation schemes on the numerical solution and emphasizes the importance of accurate physics representation alongside mathematical robustness. The convergence of the numerical solver is examined concerning the nature of the studied physics, highlighting the need for appropriate relaxation techniques. Additionally, the fractional step method is explored to solve the strong pressure-velocity coupling in the Navier-Stokes equations while considering the addition of other transport phenomena. The analysis of turbulent flows showcases the energy cascade in the Fourier space and its truncation effect due to spatial or spectral discretization, addressed by the application of simplified models, such as Large Eddy Simulation (LES), capable of approximating the solution with reduced computational cost. Furthermore, the implementation of parallel computing using the MPI standard is discussed, emphasizing its scalability and potential for addressing the growing demands of CFD analysis in engineering fields. Overall, this research provides valuable insights into numerical methods for the Navier-Stokes equations, their application to CFD, and their practical implications for engineering processe

    Minimum-dissipation model for large-eddy simulation in OpenFoam -A study on channel flow, periodic hills and flow over cylinder

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    The minimum-dissipation model is applied to turbulent channel flows up to Reτ=2000Re_\tau = 2000, flow past a circular cylinder at Re=3900Re=3900, and flow over periodic hills at Re=10595Re=10595. Numerical simulations are performed in OpenFOAM which is based on finite volume methods for discretizing partial differential equations. We use both symmetry-preserving discretizations and standard second-order accurate discretization methods in OpenFOAM on structured meshes. The results are compared to DNS and experimental data. The results of channel flow mainly demonstrate the static QR model performs equally well as the dynamic models while reducing the computational cost. The model constant C=0.024C=0.024 gives the most accurate prediction, and the contribution of the sub-grid model decreases with the increase of the mesh resolution and becomes very small (less than 0.2 molecular viscosity) if the fine meshes are used. Furthermore, the QR model is able to predict the mean and rms velocity accurately up to Reτ=2000Re_\tau = 2000 without a wall damping function. The symmetry-preserving discretization outperforms the standard OpenFOAM discretization at Reτ=1000Re_\tau=1000. The results for the flow over a cylinder show that mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data. The symmetry-preserving scheme with the QR model predicts the best results. The various comparisons carried out for flows over periodic hills demonstrate the need to use the symmetry-preserving discretization or central difference schemes in OpenFOAM in combination with the minimum dissipation model. The model constant of C=0.024C=0.024 is again the best one

    Dynamical tides in Jupiter and the role of interior structure

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    Context. The Juno spacecraft has obtained highly accurate tidal Love numbers, which provide important constraints on the tidal response and interior structure of Jupiter. Aims. In order to exploit these observations, it is necessary to develop an approach for accurately calculating the tidal response of Jupiter for a given interior model and to investigate the role of interior structure. Methods. We directly solve the linearized tidal equations of a compressible, self-gravitating, rotating and viscous fluid body using a pseudo-spectral method. The Coriolis force is fully taken into account but the centrifugal effect is neglected. We can simultaneously obtain the real and imaginary parts of the tidal Love numbers for a given planetary interior model. Results. We calculate the tidal responses for three simple interior models of Jupiter which may contain a compact rigid core or an extended dilute core. All of models we consider can explain the fractional correction Δk22≈−4%\Delta k_{22}\approx -4\% due to dynamical tides, but all have difficulties to reconcile the observed Δk42≈−11%\Delta k_{42}\approx -11\% for the high-degree tidal Love number. We show that the Coriolis force significantly modifies gravity modes in an extended dilute core at the tidal frequency relevant to the Galilean satellites. We demonstrate that a thin stable layer in the outer region, if exists, would also influence the tidal responses of Jupiter.Comment: Accepted for publication in A&

    Coordinate-Descent Augmented Lagrangian Methods for Interpretative and Adaptive Model Predictive Control

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    Model predictive control (MPC) of nonlinear systems suffers a trade-off between model accuracy and real-time compu- tational burden. This thesis presents an interpretative and adaptive MPC (IA-MPC) framework for nonlinear systems, which is related to the widely used approximation method based on successive linearization MPC and Extended Kalman Filtering (SL-MPC-EKF). First, we introduce a solution algo- rithm for linear MPC that is based on the combination of Co- ordinate Descent and Augmented Lagrangian (CDAL) ideas. The CDAL algorithm enjoys three features: (i) it is construction-free, in that it avoids explicitly constructing the quadratic pro-gramming (QP) problem associated with MPC; (ii) is matrix-free, as it avoids multiplications and factorizations of matri-ces; and (iii) is library-free, as it can be simply coded without any library dependency, 90-lines of C-code in our implemen-tation. We specialize the algorithm for both state-space for-mulations of MPC and formulations based on AutoRegres-sive with eXogenous terms models (CDAL-ARX). The thesis also presents a rapid-prototype MPC tool based on the gPROMS platform, in which the qpOASES and CDAL algorithm was integrated. In addition, based on an equivalence between SS-based and ARX-based MPC problems we show,we investigate the relation between the proposed IA-MPC and the classical SL-MPC-EKF method. Finally, we test and show the effectiveness of the proposed IA-MPC frameworkon four typical nonlinear MPC benchmark examples
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