A Multi-Fluid Investigation of the Membrane Supporting Grid Effects on the Richtmyer-Meshkov Instability

2019 ◽  
Vol 390 ◽  
pp. 1-7
Author(s):  
Mohamad Al-Marouf ◽  
Ravi Samtaney
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Complex Geometry ◽  
Adaptive Mesh ◽  
Circular Cylinders ◽  
Small Scale ◽  
Gas Mixture ◽  
Material Interface ◽  
Wire Grid ◽  
Thin Wires

We present results of numerical experiments performed to evaluate the effects of the material interface supporting wire grid on the Richtmyer-Meshkov instability (RMI). An air-SF6 interface initially perturbed sinusoidally supported on a number of solid circular cylinders. These cylinders are introduced along the interface to mimic the presence of the grid thin wires. The resulted mixing and growth rate of the perturbation in the presence and absence of the supporting grid were analyzed and validated with experimental measurements. The small scales perturbation imposed by the cylinders are around two orders of magnitude smaller than the interface sinusoidal perturbation wavelength requiring the adaptive mesh refinement (AMR) to adequately resolve small scale features. Furthermore, an embedded boundary technique is used to handle the complex geometry stemming from the presence of these multiple. A multi-fluid formulation is utilized to form a multi-gas species interface and compute the gas mixture properties.

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

scholarly journals Ultrahigh-resolution model of a breakout CME embedded in the solar wind

2018 ◽  
Vol 620 ◽  
pp. A57 ◽  
Author(s):  
S. Hosteaux ◽  
E. Chané ◽  
B. Decraemer ◽  
D.-C. Talpeanu ◽  
S. Poedts
Keyword(s):  
Solar Wind ◽  
Adaptive Mesh Refinement ◽  
Flux Rope ◽  
Adaptive Mesh ◽  
Electrical Current ◽  
Substantial Effect ◽  
Small Scale ◽  
Release Process ◽  
Ultrahigh Resolution ◽  
Current Sheets

Aims. We investigate the effect of a background solar wind on breakout coronal mass ejections, in particular, the effect on the different current sheets and the flux rope formation process. Methods. We obtained numerical simulation results by solving the magnetohydrodynamics equations on a 2.5D (axisymmetric) stretched grid. Ultrahigh spatial resolution is obtained by applying a solution adaptive mesh refinement scheme by increasing the grid resolution in regions of high electrical current, that is, by focussing on the maximum resolution of the current sheets that are forming. All simulations were performed using the same initial base grid and numerical schemes; we only varied the refinement level. Results. A background wind that causes a surrounding helmet streamer has been proven to have a substantial effect on the current sheets that are forming and thus on the dynamics and topology of the breakout release process. Two distinct ejections occur: first, the top of the helmet streamer detaches, and then the central arcade is pinched off behind the top of the helmet streamer. This is different from the breakout scenario that does not take the solar wind into account, where only the central arcade is involved in the eruption. In the new ultrahigh-resolution simulations, small-scale structures are formed in the lateral current sheets, which later merge with the helmet streamer or reconnect with the solar surface. We find that magnetic reconnections that occur at the lateral breakout current sheets deliver the major kinetic energy contribution to the eruption and not the reconnection at the so-called flare current sheet, as was seen in the case without background solar wind.

Tsunami modelling with adaptively refined finite volume methods

Acta Numerica ◽  
2011 ◽  
Vol 20 ◽  
pp. 211-289 ◽  
Author(s):  
Randall J. LeVeque ◽  
David L. George ◽  
Marsha J. Berger
Keyword(s):  
Finite Volume ◽  
Adaptive Mesh Refinement ◽  
Spatial Scales ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Small Scale ◽  
Tsunami Propagation ◽  
Small Perturbations ◽  
Tsunami Modelling ◽  
Two Space Dimensions

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a ‘wellbalanced’ manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows.

An Embedded Ghost-Fluid Method for Compressible Flow in Complex Geometry

2016 ◽  
Vol 366 ◽  
pp. 31-39
Author(s):  
M. Al-Marouf ◽  
R. Samtaney
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Solutions ◽  
Complex Geometry ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Ghost Fluid Method ◽  
Structured Adaptive Mesh Refinement ◽  
Number Flow ◽  
High Mach

We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. The PDE multidimensional extrapolation approach of Aslam [1] is used to reconstruct the solution in the ghost-fluid regions and impose boundary conditions at the fluid-solid interface. The CNS equations are numerically solved by the second order multidimensional upwind method of Colella [2] and Saltzman [3]. Block-structured adaptive mesh refinement implemented under the Chombo framework is utilized to reduce the computational cost while keeping high-resolution mesh around the embedded boundary and regions of high gradient solutions. Numerical examples with different Reynolds numbers for low and high Mach number flow will be presented. We compare our simulation results with other reported experimental and computational results. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

scholarly journals What determines the formation and characteristics of protoplanetary discs?

2020 ◽  
Vol 635 ◽  
pp. A67 ◽  
Author(s):  
Patrick Hennebelle ◽  
Benoit Commerçon ◽  
Yueh-Ning Lee ◽  
Sébastien Charnoz
Keyword(s):  
Adaptive Mesh Refinement ◽  
Initial Conditions ◽  
Adaptive Mesh ◽  
Small Scale ◽  
Initial Structure ◽  
Solar Mass ◽  
Central Object ◽  
The Impact ◽  
Protoplanetary Discs

Context. Planets form in protoplanetary discs. Their masses, distribution, and orbits sensitively depend on the structure of the protoplanetary discs. However, what sets the initial structure of the discs in terms of mass, radius and accretion rate is still unknown. Aims. It is therefore of great importance to understand exactly how protoplanetary discs form and what determines their physical properties. We aim to quantify the role of the initial dense core magnetisation, rotation, turbulence, and misalignment between rotation and magnetic field axis as well as the role of the accretion scheme onto the central object. Methods. We performed non-ideal magnetohydrodynamics numerical simulations using the adaptive mesh refinement code Ramses of a collapsing, one solar mass molecular core to study the disc formation and early, up to 100 kyr, evolution. We paid particular attention to the impact of numerical resolution and accretion scheme. Results. We found that the mass of the central object is almost independent of the numerical parameters such as the resolution and the accretion scheme onto the sink particle. The disc mass and to a lower extent its size, however heavily depend on the accretion scheme, which we found is itself resolution dependent. This implies that the accretion onto the star and through the disc are largely decoupled. For a relatively large domain of initial conditions (except at low magnetisation), we found that the properties of the disc do not change too significantly. In particular both the level of initial rotation and turbulence do not influence the disc properties provide the core is sufficiently magnetised. After a short relaxation phase, the disc settles in a stationary state. It then slowly grows in size but not in mass. The disc itself is weakly magnetised but its immediate surrounding on the contrary is highly magnetised. Conclusions. Our results show that the disc properties directly depend on the inner boundary condition, i.e. the accretion scheme onto the central object. This suggests that the disc mass is eventually controlled by a small-scale accretion process, possibly the star-disc interaction. Because of ambipolar diffusion and its significant resistivity, the disc diversity remains limited and except for low magnetisation, their properties are weakly sensitive to initial conditions such as rotation and turbulence.

Scalable Structured Adaptive Mesh Refinement with Complex Geometry

2017 ◽  
pp. 307-318
Author(s):  
Brian Van Straalen ◽  
David Trebotich ◽  
Andrey Ovsyannikov ◽  
Daniel T. Graves
Keyword(s):  
Adaptive Mesh Refinement ◽  
Complex Geometry ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Structured Adaptive Mesh Refinement

scholarly journals New boundary conditions for simulating the filling stage of the injection molding process

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wagner de Campos Galuppo ◽  
Ana Magalhães ◽  
Luís Lima Ferrás ◽  
João Miguel Nóbrega ◽  
Célio Fernandes
Keyword(s):  
Injection Molding ◽  
Boundary Conditions ◽  
Adaptive Mesh Refinement ◽  
Complex Geometry ◽  
Real Life ◽  
Adaptive Mesh ◽  
Injection Molding Process ◽  
Molding Process ◽  
Content Type ◽  
Filling Stage

Purpose The purpose of this paper is to develop new boundary conditions for simulating the injection molding process of polymer melts. Design/methodology/approach The boundary conditions are derived and implemented to simulate real-life air vents (used to allow the air escape from the mold). The simulations are performed in the computational library OpenFOAM® by considering two different fluid models, namely, Newtonian and generalized Newtonian (Bird–Carreau model). Findings A detailed study on the accuracy of the solver interFoam for simulating the filling stage is presented, by considering simple geometries and adaptive mesh refinement. The verified code is then used to study the three-dimensional filling of a more complex geometry. Originality/value The results obtained showed that the numerical method is stable and allows one to model the filling process, simulating the real injection molding process.

Adaptive mesh refinement method based investigation of the interaction between shock wave, boundary layer, and tip vortex in a transonic compressor

2017 ◽  
Vol 232 (4) ◽  
pp. 694-715 ◽  
Author(s):  
Jinlan Gou ◽  
Xin Yuan ◽  
Xinrong Su
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Tip Vortex ◽  
Small Scale ◽  
Tip Leakage ◽  
Transonic Compressor ◽  
Mesh Convergence

Shock wave and tip leakage are important flow features at small length scales. These flow phenomena and their interactions play important roles in the performance of modern transonic fans and compressors. In most numerical predictions of these features, mesh convergence studies are conducted using overall performance data as criteria. However, less effort is made in assessing the quality of the predicted small-scale features using a mesh that yields a fairly accurate overall performance. In this work, this problem is addressed using the adaptive mesh refinement (AMR) method, which automatically refines the local mesh and provides very high resolution for the small-scale flow feature, at much less cost compared with globally refining the mesh. An accurate and robust AMR system suitable for turbomachinery applications is developed in this work and the widely studied NASA Rotor-37 case is investigated using the current AMR method. The complex interactions between the shock wave and the boundary layer, as well as those between the shock wave and the tip vortex, are accurately captured by AMR with a very high local grid resolution, and the flow mechanisms are analyzed in detail. The baseline mesh, which is considered to be “acceptable” according to the commonly used mesh convergence study, is unable to capture the detailed interaction between the shock wave and the boundary layer. Moreover, it falsely predicts the tip leakage vortex breakdown, which is a consequence of inadequate resolution in the tip region. Current work highlights the importance of a careful check of the mesh convergence, if small-scale features are the primary concern. The AMR method developed in this work successfully captures the flow details in the transonic compressor in an automatic fashion, and has been verified to be efficient compared with the globally mesh refinement or manually mesh regeneration.

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