The use of adaptive spatial resolution to simulate flows of practical interest using Smoothed Particle Hydrodynamics (SPH) is of considerable importance. Recently, Muta and Ramachandran [1] have proposed an efficient adaptive SPH method which is capable of handling large changes in particle resolution. This allows the authors to simulate problems with much fewer particles than was possible earlier. The method was not demonstrated or tested with moving bodies or multiple bodies. In addition, the original method employed a large number of background particles to determine the spatial resolution of the fluid particles. In the present work we establish the formulation's effectiveness for simulating flow around stationary and moving geometries. We eliminate the need for the background particles in order to specify the geometry-based or solution-based adaptivity and we discuss the algorithms employed in detail. We consider a variety of benchmark problems, including the flow past two stationary cylinders, flow past different NACA airfoils at a range of Reynolds numbers, a moving square at various Reynolds numbers, and the flow past an oscillating cylinder. We also demonstrate different types of motions using single and multiple bodies. The source code is made available under an open source license, and our results are reproducible.
We present qualitative observations on the internal flow characteristics of fluidic oscillator geometries commonly referred to as sweeping jets in active flow control applications. This is part of the fluid dynamics videos.
Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous media, and approximates a solid object in the limit of vanishing porosity. In its simplest form, the momentum equations are augmented by a term penalizing the fluid velocity, yielding good results in many applications. However, it induces numerical stiffness, especially if high-pressure gradients need to be balanced. Here, we focus on the effect of the reduce…
We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The Reynolds number is held at $Re{\approx}300$ to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbour-induced hydrodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on dra…
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Equipped with a fluid-solid coupling framework that integrates high-order temporal and spatial discretization schemes, numerical experiments concerning flow involving stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions, as well as subsonic and su…
We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of the convective terms in the Navier-Stokes equations relies on a robust energy-preserving numerical flux, and numerical diffusion inherited from the AUSM scheme is added limited to the vicinity of shock waves, or wherever spurious numerical oscillations are sensed. The solver is capable of conserving the total kinetic energy in the inviscid limit, and it bears…
To study simultaneously the hydrodynamic and thermodynamic behaviors in compressible flow systems with spherical or cylindrical symmetry, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical or cylindrical symmetry in spherical or cylindrical coordinates. To this aim, a key technique is to use \emph{local} Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright . Even though the hydrodynamic models …
In this paper, an SPH method based on the SPH-ALE formulation is used for modelling two-phase flows with large density ratios and realistic sound speeds. The SPH scheme is further improved to circumvent the tensile instability that may occur in the SPH simulations. The two-phase SPH solver is then used to model a benchmark problem of liquid impact on a rigid wall. The results are compared with an incompressible Level Set solver. Furthermore, a wave impact on a rigid wall with a large entrained air pocket is modelled. The SPH simulation is initialised by the output of a fully non-linear potenti…
This paper sums up some recent validations of an immersed boundary method for compressible flow simulations. It has been already shown that this method is able to provide accurate results without meshing effort around more or less complex geometries. Here, the authors focus on several simple test cases to assess the application range of the method. From subsonic to hypersonic flows, from steady to large-eddy unsteady simulations, in 2D or 3D, results are compared to classical simulations with body-fitted meshes and experiment. Moreover, the use of an efficient Navier-Stokes solver for all the …
To kinetically model implosion and explosion related phenomena, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical symmetry in spherical coordinates. To this aim, a key technique is to use \emph{local} Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a Discrete Ve…
In this paper we propose an accurate, and computationally efficient method for incorporating adaptive spatial resolution into weakly-compressible Smoothed Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged in an accurate manner. Critically, the method ensures that the number of neighbors of each particle is optimal, leading to an efficient algorithm. A set of background particles is used to specify either geometry-based spatial resolution, where the resolution is a function of distance to a solid body, or solution-based adaptive resolution, where the resolution is …
An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods. Moreover, two Faxén relations of next-higher order beyond the stresslet are calculated explicitly for compressible media. They quantify higher-order moments involving the force distribution on rigid particles in a deformed elastic medium. Additionally, the displaceability and rotateability matrices are calculated up to (including) sixth order in inverse particle separation d…
The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen-Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number $\mathcal{M}_\infty$. JREs were carried out with terms polynomial in the inverse radius $r^{-1}$ to high orders in two dimensions (2D), but were limited to order $\mathcal{M}_\infty^4$ in three dimensions (3D). We derive general JRE formulae to arbitrary order, adiabatic index, and dimension. We find that powers of $\ln(r)$ can creep into the expansion, and are essential in 3D beyond order $\mathcal{M}_\infty^4…
The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) formulation coupled to new non-reflecting outflow boundary conditions. A large-eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a 90 grades pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bend…
The goal of this report is to present the final project conducted in order to fulfill the requirements of the M.Sc. degree at the Department of Mechanical Engineering, Ben-Gurion University (BGU) of the Negev. The project comprises theoretical research investigating natural convection compressible flow with high temperature differences and with complex geometries. The research motivation comes from long-term research investigating and simulating the steady state and transient multiphase flow regimes existing in the reactor core, that was established by the Soreq Nuclear Center. The main object…
A fully-implicit solving approach to an adaptive multi-scale model -- coupling a vertical-equilibrium and full-dimensional model for compressible, multi-phase flow in porous media
A new smoothed particle hydrodynamics method based on high-order moving-least-square targeted essentially non-oscillatory scheme for compressible flows
The Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) method is a Lagrangian method that is typically used for the simulation of incompressible fluids. While developing an SPH-based scheme or solver, researchers often verify their code with exact solutions, solutions from other numerical techniques, or experimental data. This typically requires a significant amount of computational effort and does not test the full capabilities of the solver. Furthermore, often this does not yield insights on the convergence of the solver. In this paper we introduce the method of manufactured solutio…
Compressible flows around blunt objects have diverse applications, but present analytic treatments are inaccurate and limited to narrow parameter regimes. We show that the flow in front of an axisymmetric body is accurately derived analytically using a low order expansion of the perpendicular gradients in terms of the parallel velocity. This reproduces both subsonic and supersonic flows measured and simulated for a sphere, including the transonic regime and the bow shock properties.
We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively forced spherical particle with a known analytical solution. The simulation also gives information about the fluid motion, which provides some insight into the particle motion. Fluctuations are also introduced by random stress, and the validity of this case is examined by comparing the calculation results with the fluctuation-dissipation theorem.
This paper proposes and validates two new particle regularization techniques for the Smoothed Particle Hydrodynamics (SPH) numerical method to improve its stability and accuracy for free surface flow simulations. We introduce a general form of the Dynamic pair-wise Particle Collision (DPC) regularization technique that we recently proposed in the context of the Moving Particle Semi-implicit (MPS) method in [1]. The DPC coupled with the standard Particle Shifting (PS) technique has given rise to a hybrid approach that we propose to alleviate particle clustering issues in the free-surface and sp…
We propose a scheme of acoustic spherical cloaking by means of background irrotational flow in compressible fluid. The background flow forms a virtual curved spacetime and guides the sound waves bypass the cloaked objects. To satisfy the laws of real fluid, we show that spatially distributed mass source and momentum source are necessary to supply. The propagation of sound waves in this system is studied via both geometric acoustics approximation and full wave approach. The analytic solution of sound fields is obtained for plane wave incidence. The results reveal the effect of phase retardation…
The surface winds of Jupiter and Saturn are primarily zonal. Each planet exhibits strong prograde equatorial flow flanked by multiple alternating zonal winds at higher latitudes. The depth to which these flows penetrate has long been debated and is still an unsolved problem. Previous rotating convection models that obtained multiple high latitude zonal jets comparable to those on the giant planets assumed an incompressible (Boussinesq) fluid, which is unrealistic for gas giant planets. Later models of compressible rotating convection obtained only few high latitude jets which were not amenable…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. We obtain a detailed description of the geometry of this singular bo…
General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\sim e^{-Γt}, Γ>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $Γ\approx \frac{A}ε \frac{We}{ε^{2}} \exp(-B \frac{We}{ε^2})$, where $0<ε\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants. In this paper, we prove this conjecture and calculate $A$ and $B$ to leading order in $ε$.
Solving nonlinear subsonic compressible flow in infinite domain via multi-stage neural networks
Washington University in St. Louis（华盛顿大学圣路易斯分校）；University of Notre Dame（诺特大学）；Central South University（中南大学）；Stanford University（斯坦福大学）；New York University（纽约大学）
Global Well-Posedness of the Vacuum Free Boundary Problem for the Degenerate Compressible Navier-Stokes Equations With Large Data of Spherical Symmetry
We present an $rp$-adaptation strategy for high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to $r$-adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simul…
To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourth-order subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible flows over (unstructured) triangular meshes was developed to improve the compactness and efficiency. Compared to the fourth-order GKS-based traditional finite volume (FV) method, the proposed method realizes compactness effectively by subdividing each cell into a set of subcells or control volumes (CVs) and selecting only face-neighboring cells for high-order co…
