150 research outputs found

    Turbulence: Numerical Analysis, Modelling and Simulation

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    The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps

    High-order methods for diffuse-interface models in compressible multi-medium flows: a review

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    The diffuse interface models, part of the family of the front capturing methods, provide an efficient and robust framework for the simulation of multi-species flows. They allow the integration of additional physical phenomena of increasing complexity while ensuring discrete conservation of mass, momentum, and energy. The main drawback brought by the adoption of these models consists of the interface smearing, increasing with the simulation time, therefore, requiring a counteraction through the introduction of sharpening terms and a careful selection of the discretization level. In recent years, the diffuse interface models have been solved using several numerical frameworks including finite volume, discontinuous Galerkin, and hybrid lattice Boltzmann method, in conjunction with shock and contact wave capturing schemes. The present review aims to present the recent advancements of high-order accuracy schemes with the capability of solving discontinuities without the introduction of numerical instabilities and to put them in perspective for the solution of multi-species flows with the diffuse interface method.Engineering and Physical Sciences Research Council (EPSRC): 2497012. Innovate UK: 263261. Airbus U

    Riemann solvers with non-ideal thermodynamics: exact, approximate, and machine learning solutions

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    The Riemann problem is an important topic in the numerical simulation of compressible flows, aiding the design and verification of numerical codes. A limitation of many of the existing studies is the perfect gas assumption. Over the past century, flow technology has tended toward higher pressures and temperatures such that non-ideal state equations are required along with specific heats, enthalpy, and speed of sound dependent on the full thermodynamic state. The complexity of the resulting physics has compelled researchers to compromise on rigour in favour of computational efficiency when studying non-ideal shock and expansion waves. This thesis proposes exact, approximate, and machine learning approaches that balance accuracy and computational efficiency to varying degrees when solving the Riemann problem with non-ideal thermodynamics. A longstanding challenge in the study of trans- and supercritical flows is that numerical simulations are often validated against prior numerical simulations or inappropriate ideal-gas shock tube test cases. The lack of suitable experimental data or adequate reference solutions means that existing studies face difficulties distinguishing numerical inaccuracies from the physics of the problem itself. To address these shortcomings, a novel derivation of exact solutions to shock and expansion waves with arbitrary equation of state is performed. The derivation leverages a domain mapping from space-time coordinates to characteristic wave coordinates. The solutions may be integrated into a suitable Riemann solution algorithm to produce exact reference solutions that do not require numerical integration. The study of wave structures is also pertinent to the development of practical Riemann solvers for finite volume codes, which must be computationally simple yet entropy-stable. Using the earlier derivations, the idea of structurally complete approximate Riemann solvers (StARS) is proposed. StARS provides an efficient means for analytically restoring the isentropic expansion wave to pre-existing three-wave solvers with arbitrary thermodynamics. The StARS modification is applied to a Roe scheme and shown to have improved accuracy but comparable computational speed to the popular Harten-Hyman entropy fix. Four test cases are examined: a transcritical shock tube, a shock tube with periodic bounds that produce interfering waves, a two-dimensional Riemann problem, and a gradient Riemann problem---a variant on the traditional Riemann problem featuring an initial gradient of varying slope rather than an initial step function. Additionally, a scaling analysis shows that entropy violations are most prevalent and yield the greatest errors in trans- and supercritical flows with large gradients. The final area of inquiry focuses on FluxNets, that is, learning-based Riemann solvers whose accuracy and efficiency fall in between those of exact and approximate solvers. Various approaches to the design and training of fully connected neural networks are assessed. By comparing data-driven versus physics-informed loss functions, as well as neural networks of varying size, the results show that order-of-magnitude reductions in error compared to the Roe solver can be achieved with relatively compact architectures. Numerical validation on a transcritical shock tube test case and two-dimensional Riemann problem further reveal that a physics-informed approach is critical to ensuring smoothness, generalizability, and physical consistency of the resulting numerical solutions. Additionally, parallelization can be leveraged to accelerate inference such that the significant gains in accuracy are achieved at one quarter the runtime of exact solvers. The trade-off in accuracy versus efficiency may be justified in the case of non-ideal flows where even minor errors can result in spurious oscillations and destabilized solutions

    Detailed simulations of bubble-cluster dynamics

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    The violent collapse of bubble clusters can be an important mechanism of damage to adjacent material surfaces in both engineering and biomedical applications. Because of their complexity, past theoretical studies have generally been restricted to significantly simplified models, such as homogenized continuum models based upon volume averages or arrays of strictly spherical bubbles, which neglect detailed bubble dynamics. However, the details of the bubble-scale dynamics are potentially important locally. For example, wall or tissue damage is expected to depend upon peak pressures rather than the average pressure that might be computed with a homogeneous model. Here, we simulate the expansion and subsequent collapse of hemispherical clusters of 50 bubbles adjacent to a planar rigid wall and viscous fluids as models for soft tissues in therapeutic ultrasound using a computationally efficient diffuse-interface numerical scheme for compressible multiphase flows. It represents in detail the coupled asymmetric dynamics of each bubble within the cluster. The development of this scheme and its application to simulate detailed bubble-cloud collapse are the principal contributions of this dissertation. The numerical scheme represents multi-fluid interfaces using field variables (interface functions) with associated transport equations. In our formulation, these are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in our method is that the interface regularization is asymptotically compatible with the thermodynamic laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. The finite-volume numerical solver is also integrated in a multi-resolution Adaptive Mesh Refinement (AMR) framework that allows efficient resolution of individual bubbles of the cluster in a sufficiently large domain. We first quantify the improved convergence of this formulation in an air-helium shock-tube problem and an air-water bubble-collapse problem, then show that it enables fundamentally better simulations of single-bubble dynamics. Demonstrations include both a spherical-bubble collapse, which facilitates comparison with a semi-analytic solution, and a jetting-bubble collapse adjacent a wall. For the spherical collapse, we show agreement with the semi-analytic solution, and the preservation of symmetry despite the Cartesian mesh. Comparisons for the near-wall case show that without the new formulation the re-entrant jet is suppressed by numerical diffusion leading to qualitatively incorrect results. Next, the method is applied to simulate cluster dynamics adjacent to material surfaces. Simulations near the rigid wall show that collapse propagates inward, and a geometrical pressure focusing occurs, which generates impulsive pressures near the focus. The peak pressures depend strongly on the arrangement of the bubbles, particularly those near the focus. The initial acceleration of the bubbles that drives their expansion is identified as an important parameter governing the bubble interactions, and hence the pressure focusing. The simplified models we compare with provide good agreement for the gross cluster behavior, for example gas volume history, but fail to predict the same peak pressures seen in the detailed simulations during the collapse. Replacing the rigid wall with a viscous fluid, as a crude model for tissue, shows significantly different dynamics compared to the rigid wall. Simulations show weaker pressure focusing with substantially lower peak pressures

    Numerical methods with controlled dissipation for small-scale dependent shocks

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    We provide a ‘user guide' to the literature of the past twenty years concerning the modelling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes of problems and solutions: nonclassical undercompressive shocks, hyperbolic systems in nonconservative form, and boundary layer problems. We review the relevant models arising in continuum physics and describe the numerical methods that have been proposed to capture small-scale dependent solutions. In agreement with general well-posedness theory, small-scale dependent solutions are characterized by a kinetic relation, a family of paths, or an admissible boundary set. We provide a review of numerical methods (front-tracking schemes, finite difference schemes, finite volume schemes), which, at the discrete level, reproduce the effect of the physically meaningful dissipation mechanisms of interest in the applications. An essential role is played by the equivalent equation associated with discrete schemes, which is found to be relevant even for solutions containing shock wave

    The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

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    Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data
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