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 Conservative Modification to the Ghost Fluid Method for Compressible Multiphase Flows

2011 ◽  
Vol 10 (4) ◽  
pp. 785-806 ◽  
Author(s):  
Wei Liu ◽  
Li Yuan ◽  
Chi-Wang Shu
Keyword(s):  
Multiphase Flows ◽  
Time Discretization ◽  
Weno Scheme ◽  
Third Order ◽  
Ghost Fluid Method ◽  
Material Interface ◽  
Numerical Resolution ◽  
Runge Kutta Method ◽  
Modification Procedure ◽  
Fifth Order

AbstractA conservative modification to the ghost fluid method (GFM) is developed for compressible multiphase flows. The motivation is to eliminate or reduce the conservation error of the GFM without affecting its performance. We track the conservative variables near the material interface and use this information to modify the numerical solution for an interfacing cell when the interface has passed the cell. The modification procedure can be used on the GFM with any base schemes. In this paper we use the fifth order finite difference WENO scheme for the spatial discretization and the third order TVD Runge-Kutta method for the time discretization. The level set method is used to capture the interface. Numerical experiments show that the method is at least mass and momentum conservative and is in general comparable in numerical resolution with the original GFM.

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.

scholarly journals Computational Evaluation of Shock Wave Interaction with a Cylindrical Water Column

2021 ◽  
Vol 11 (11) ◽  
pp. 4934
Author(s):  
Viola Rossano ◽  
Giuliano De Stefano
Keyword(s):  
Shock Wave ◽  
Water Column ◽  
Wave Interaction ◽  
Navier Stokes ◽  
Plane Shock ◽  
Governing Equations ◽  
Computational Evaluation ◽  
Air Water Interface ◽  
The Mean ◽  
The Impact

Computational fluid dynamics was employed to predict the early stages of the aerodynamic breakup of a cylindrical water column, due to the impact of a traveling plane shock wave. The unsteady Reynolds-averaged Navier–Stokes approach was used to simulate the mean turbulent flow in a virtual shock tube device. The compressible flow governing equations were solved by means of a finite volume-based numerical method, where the volume of fluid technique was employed to track the air–water interface on the fixed numerical mesh. The present computational modeling approach for industrial gas dynamics applications was verified by making a comparison with reference experimental and numerical results for the same flow configuration. The engineering analysis of the shock–column interaction was performed in the shear-stripping regime, where an acceptably accurate prediction of the interface deformation was achieved. Both column flattening and sheet shearing at the column equator were correctly reproduced, along with the water body drift.

EMISSION BY UNDERWATER EXPLOSIONS

Geophysics ◽  
1970 ◽  
Vol 35 (3) ◽  
pp. 419-435 ◽  
Author(s):  
M. Lavergne
Keyword(s):  
Shock Wave ◽  
Frequency Band ◽  
Experimental Investigations ◽  
Water Interface ◽  
Single Charge ◽  
Seismic Effects ◽  
Underwater Explosions ◽  
Seismic Efficiency ◽  
Marine Life ◽  
Air Water Interface

Theoretical and experimental investigations of the seismic effects of underwater explosions of dynamite charges are described. We investigate the acoustic efficiency in a broad frequency band and in the seismic frequency band, the partition of energy between the shock wave and bubble pulses, the seismic effects of cavitation due to ghost reflection at the air‐water interface, and the damage caused to marine life. Results concerning the variation of the seismic efficiency with shot conditions are given: the conclusion is that the seismic efficiency of charges of the order of 100 gm can be considerably increased by dividing the charges and by shooting at depth. Experiments show that two or three properly spaced 50 gm charges of dynamite, shot at a depth of about 12 m, give the same result as a single charge of about 5 to 15 kg shot at a depth of 1 m. CDP marine sections comparing caged charge shooting with conventional shooting in the same area are shown.

Numerical Simulation of Shock Wave in Air Based on FCT Method

2013 ◽  
Vol 397-400 ◽  
pp. 270-273
Author(s):  
Ying Li ◽  
Xiao Bin Li ◽  
Yu Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Comparative Analysis ◽  
Numerical Method ◽  
Blast Wave ◽  
Empirical Formula ◽  
Godunov Method ◽  
Numerical Accuracy

Blast wave is numerical simulated based on FCT method. According to the comparative analysis, taking Henrych empirical formula as a standard, FCT method is more accuracy than Godunov method. Moreover, it has been found that the numerical accuracy is insufficient when the distance is small, it is necessary to develop and modify the numerical method continuously.

High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

2015 ◽  
Vol 25 (08) ◽  
pp. 1553-1588 ◽  
Author(s):  
Yan Jiang ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Random Walk ◽  
Finite Difference ◽  
Temporal Integration ◽  
Time Discretization ◽  
High Order ◽  
Correlated Random Walk ◽  
Third Order ◽  
Positivity Preserving ◽  
Fifth Order ◽  
High Order Finite Difference

In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

scholarly journals Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Time Discretization ◽  
Neumann Condition ◽  
Integral Boundary ◽  
Semilinear Heat Equation ◽  
Rothe Method ◽  
The Given

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.

scholarly journals FAST MESH INTERPOLATION AND MESH DECOMPOSITION WITH APPLICATIONS

2012 ◽  
Vol 12 (01) ◽  
pp. 1250006
Author(s):  
SHUHUA LAI ◽  
FUHUA (FRANK) CHENG
Keyword(s):  
Iterative Process ◽  
Interpolation Method ◽  
Low Frequency ◽  
Texture Mapping ◽  
Construction Process ◽  
Mesh Decomposition ◽  
Decomposition Scheme ◽  
New Approaches ◽  
Control Mesh ◽  
The Given

A new approach for constructing a smooth subdivision surface to interpolate the vertices of an arbitrary mesh is presented. The construction process does require setting up neither any linear systems, nor any matrix computation, but is simply done by iteratively moving vertices of the given mesh locally until control mesh of the required interpolating surface is reached. The new interpolation method has the simplicity of a local method in effectively dealing with meshes of a large number of vertices. It also has the capability of a global method in faithfully resembling the shape of a given mesh. Furthermore, the new method is fast and does not require a fairing step in the construction process because the iterative process converges to a unique solution at an exponential rate. Another important result of this work is, with the new iterative process, each mesh (surface) can be decomposed into a sum of simpler meshes (surfaces) which carry high-and low-frequency information of the given model. This mesh decomposition scheme provides us with new approaches to some classic applications in computer graphics such as texture mapping, denoising/smoothing/sharpening, and morphing. These new approaches are demonstrated in this paper and test results are included.

The Application of Adaptive Wavelet Method to Multi-Dimensional Limiting Process for Enhancement of Computational Efficiency

2011 ◽  
Author(s):  
Hyungmin Kang ◽  
Kyunghyun Park ◽  
Dongho Lee ◽  
Kyuhong Kim ◽  
Seunghwan Park ◽  
...  
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Higher Order ◽  
High Order ◽  
Computational Time ◽  
Numerical Accuracy ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
Computational Fluid Dynamics Cfd ◽  
Adaptive Wavelet Method

An adaptive wavelet method is applied in order to enhance the computational efficiency of enhanced Multi-dimensional Limiting Process (e-MLP) without deterioration of the numerical accuracy of original Computational Fluid Dynamics (CFD) scheme. For this purpose, higher order of adaptive wavelet method is constructed including higher order of wavelet decomposition and modified thresholding. Besides, the locations of crucial features such as shock, vortex core, etc. are automatically and accurately searched in the CFD dataset through wavelet transformation. Only on these locations, high order spatial interpolation scheme with e-MLP are performed; in the other locations, interpolation method is utilized to compute residual values, which reduces the computational time of flux evaluation. This high order adaptive wavelet method was applied to unsteady Euler flow computations such as shock-vortex interaction problem. Throughout these processes, it was verified that computational efficiency was enhanced with preservation of numerical accuracy of CFD solver.

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