scholarly journals A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

2021 ◽  
Author(s):  
Jonas Zeifang ◽  
Andrea Beck
Keyword(s):  
Level Set ◽  
Phase Interface ◽  
Time Discretization ◽  
Spectral Element ◽  
Computational Time ◽  
Minor Role ◽  
Ghost Fluid Method ◽  
Specific Level ◽  
Flux Splitting ◽  
Mach Numbers

AbstractConsidering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a specific level set ghost fluid method and an implicit-explicit (IMEX) flux splitting is proposed to overcome this timestep restriction. A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface. In this part of the domain, the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases. It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method. Applications to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

Simulation of Water Droplet Merging under Shock Wave Using Real Ghost Fluid Method

2013 ◽  
Vol 444-445 ◽  
pp. 628-632
Author(s):  
Ru Chao Shi ◽  
Sheng Li Xu ◽  
Ya Jun Zhang
Keyword(s):  
Shock Wave ◽  
Interpolation Method ◽  
Time Discretization ◽  
Problem Solver ◽  
Ghost Fluid Method ◽  
Numerical Accuracy ◽  
Air Water Interface ◽  
Fifth Order ◽  
The Given ◽  
Flow States

This paper presents a 3D numerical simulation of water droplets merging under a given shock wave. We couple interpolation method to RGFM (Real Ghost Fluid Method) to improve the numerical accuracy of RGFM. The flow states of air-water interface are calculated by ARPS (approximate Riemann problem solver). Flow field is solved by Euler equation with fifth-order WENO spatial discretization and fourth-order R-K (Runge-Kutta) time discretization. We also employ fifth-order HJ-WENO to discretize level set equation to keep track of gas-liquid interface. Numerical results demonstrate that droplets shape has little change before merging and the merged droplet gradually becomes umbrella-shaped under the given shock wave. We verify that combination of RGFM with interpolation method has the property of reducing numerical error by comparing to the results without employment of interpolation method.

A multiphase level-set approach for all-Mach numbers

2018 ◽  
Vol 167 ◽  
pp. 1-16 ◽  
Author(s):  
Michael P. Kinzel ◽  
Jules W. Lindau ◽  
Robert F. Kunz
Keyword(s):  
Level Set ◽  
Mach Numbers ◽  
Level Set Approach

Application of an Improved Ghost Fluid Method to the Collapse of Non-Spherical Bubbles in a Compressible Liquid

2011 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Yoshinori Jinbo
Keyword(s):  
Surface Tension ◽  
Shock Waves ◽  
Thermal Diffusion ◽  
Level Set ◽  
Compressible Liquid ◽  
Maximum Temperature ◽  
Bubble Collapse ◽  
Ghost Fluid Method ◽  
Toroidal Bubble ◽  
The Impact

The ghost fluid method (GFM) is improved to investigate violent bubble collapse in a compressible liquid, in which the adaptive mesh refinement with multigrids, the surface tension, and the thermal diffusion through the bubble interface are taken into account. The improved multigrid GFM is applied to the interaction of an incident shock wave with a bubble. The multigrid GFM captures the fine interfacial and vortex structures of the toroidal bubble when the bubble collapses violently accompanied with the penetration of the liquid jet and the formation of the shock waves. The multigrid GFM is also applied to the bubble collapse near a tissue surface in which the tissue is modeled with gelatin in order to predict the tissue damage due to the bubble collapse; the motions of three phases for the gas inside the bubble, the liquid surrounding the bubble, and the gelatin boundary are solved directly by coupling the level set method with the improved GFM. Two kinds of level set functions are utilized for distinguishing the gas-liquid interface from the liquid-gelatin interface. It is shown that the impact of the shock waves generated from the collapsing bubble on the boundary leads to the formation of depression of the boundary; the toroidal bubble penetrates into the depression. Also, the surface tension effects are successfully included in the improved GFM. The thermal effects of internal gas on the bubble collapse are also discussed by considering the thermal diffusion across the interface in the GFM. The thermal boundary layers of the toroidal bubble are captured with the method. The result shows that the smaller the initial bubble radius becomes, the lower the maximum temperature inside the bubble becomes because of the thermal diffusion across the interface.

The Characteristics-Based Matching (CBM) Method for Compressible Flow With Moving Boundaries and Interfaces

2004 ◽  
Vol 126 (4) ◽  
pp. 586-604 ◽  
Author(s):  
R. R. Nourgaliev ◽  
T. N. Dinh ◽  
T. G. Theofanous
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Level Set ◽  
Compressible Flows ◽  
Radical Change ◽  
Subsequent Paper ◽  
Ghost Fluid Method ◽  
Material Interface ◽  
Interface Position ◽  
Level Set Function

Recently, Eulerian methods for capturing interfaces in multi-fluid problems become increasingly popular. While these methods can effectively handle significant deformations of interface, the treatment of the boundary conditions in certain classes of compressible flows are known to produce nonphysical oscillations due to the radical change in equation of state across the material interface. One promising recent development to overcome these problems is the Ghost Fluid Method (GFM). The present study initiates a new methodology for boundary condition capturing in multifluid compressible flows. The method, named Characteristics-Based Matching (CBM), capitalizes on recent developments of the level set method and related techniques, i.e., PDE-based re-initialization and extrapolation, and the Ghost Fluid Method (GFM). Specifically, the CBM utilizes the level set function to capture interface position and a GFM-like strategy to tag computational nodes. In difference to the GFM method, which employs a boundary condition capturing in primitive variables, the CBM method implements boundary conditions based on a characteristic decomposition in the direction normal to the boundary. In this way overspecification of boundary conditions is avoided and we believe so will be spurious oscillations. In this paper, we treat (moving or stationary) fluid-solid interfaces and present numerical results for a select set of test cases. Extension to fluid-fluid interfaces will be presented in a subsequent paper.

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

2015 ◽  
Vol 18 (1) ◽  
pp. 203-229 ◽  
Author(s):  
Guoqiao You ◽  
Shingyu Leung
Keyword(s):  
Dynamical Systems ◽  
Level Set Method ◽  
Level Set ◽  
Limit Cycles ◽  
Time Discretization ◽  
Numerical Approach ◽  
Initial Guess ◽  
Implicit Time ◽  
Time Step ◽  
Image Regularization

AbstractWe propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions. Since the derivation is based on a semi-implicit time discretization, this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method. As an interesting application of the numerical approach, we propose a new variational approach for extracting limit cycles in dynamical systems. The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles. Further, we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

Massively Parallel Computational Fluid Dynamics With Large Eddy Simulation in Complex Geometries

2011 ◽  
Author(s):  
Andrew Duggleby ◽  
Joshua L. Camp ◽  
Yuval Doron ◽  
Paul F. Fischer
Keyword(s):  
Computer Aided Design ◽  
High Performance ◽  
Complex Geometry ◽  
Spectral Element ◽  
Computational Time ◽  
Model And Simulation ◽  
Large Eddy ◽  
Order Of Magnitude ◽  
Grid Points ◽  
Pipe Geometry

To perform complex geometry large eddy simulations in an industrially relevant timeframe, one must reduce the total time to half a day (overnight simulation). Total time includes the time of developing the mesh from the computer-aided design (CAD) model and simulation time. For reducing CAD-to-mesh time, automatic meshing algorithms can generate valid but often non-efficient meshes with often up to an order of magnitude more grid points than a custom-based mesh. These algorithms are acceptable only if paired with high-performance computing (HPC) platforms comprising thousands to millions of cores to significantly reduce computational time. Efficient use of these tools calls for codes that can scale to high processor counts and that can efficiently transport resolved scales over the long distances and times made feasible by HPC. The rapid convergence of high-order discretizations makes them particularly attractive in this context. In this paper we test the combination of automatic hexahedral meshing with a spectral element code for incompressible and low-Mach-number flows, called Nek5000, that has scaled to P >262,000 cores and sustains >70% parallel efficiency with only ≈7000 points/core. For our tests, a simple pipe geometry is used as a basis for comparing with previous fully resolved direct numerical simulations.

scholarly journals A Ghost Fluid Method Based Sharp Interface Level Set Method for Evaporating Droplet

2015 ◽  
Vol 15 ◽  
pp. 124-131 ◽  
Author(s):  
Javed Shaikh ◽  
Rajneesh Bhardwaj ◽  
Atul Sharma
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Sharp Interface ◽  
Ghost Fluid Method

scholarly journals On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sanna Mönkölä
Keyword(s):  
Fourth Order ◽  
Wave Equations ◽  
Seismic Waves ◽  
Time Discretization ◽  
Spectral Element ◽  
Higher Order ◽  
Time Stepping ◽  
Discretization Schemes ◽  
Elastic Wave Equations ◽  
Wave Problems

This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.

A mass-preserving interface-correction level set/ghost fluid method for modeling of three-dimensional boiling flows

2020 ◽  
Vol 162 ◽  
pp. 120382 ◽  
Author(s):  
B.M. Ningegowda ◽  
Zhouyang Ge ◽  
Giandomenico Lupo ◽  
Luca Brandt ◽  
Christophe Duwig
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Ghost Fluid Method
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