scholarly journals Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

2016 ◽  
Vol 19 (2) ◽  
pp. 329-353 ◽  
Author(s):  
Florian Kummer ◽  
Tim Warburton
Keyword(s):  
Discontinuous Galerkin ◽  
Level Set ◽  
Numerical Study ◽  
Level Set Methods ◽  
Computational Cost ◽  
Pressure Jump ◽  
Two Phase ◽  
Two Fluids ◽  
Whole Process ◽  
Numerical Instabilities

AbstractIn two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.

scholarly journals Discontinuous Galerkin method for solving incompressible two-phase shallow granular flow model

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987490
Author(s):  
Muhammad Rehan Saleem ◽  
Ubaid Ahmed Nisar ◽  
Shamsul Qamar
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Scheme ◽  
Flow Model ◽  
Numerical Study ◽  
Momentum Exchange ◽  
Two Phase ◽  
Runge Kutta ◽  
Model Equations

This article deals with the numerical study of two-phase shallow flow model describing the mixture of fluid and solid granular particles. The model under investigation consists of coupled mass and momentum equations for solid granular material and fluid particles through non-conservative momentum exchange terms. The non-conservativity of model equations poses major challenges for any numerical scheme, such as well balancing, positivity preservation, accurate approximation of non-conservative terms, and achievement of steady-state conditions. Thus, in order to approximate the present model an accurate, well-balanced, robust, and efficient numerical scheme is required. For this purpose, in this article, Runge–Kutta discontinuous Galerkin method is applied successfully for the first time to solve the model equations. Several test problems are also carried out to check the performance and accuracy of our proposed numerical method. To compare the results, the same model is solved by staggered central Nessyahu–Tadmor scheme. A good comparison is found between two schemes, but the results obtained by Runge–Kutta discontinuous Galerkin scheme are found superior over the central Nessyahu–Tadmor scheme.

A Sharp Surface Tension Modeling Method for Capillarity-Dominant Two-Phase Incompressible Flows

2007 ◽  
Author(s):  
Zhaoyuan Wang ◽  
Albert Y. Tong
Keyword(s):  
Surface Tension ◽  
Incompressible Flows ◽  
Jump Condition ◽  
Navier Stokes ◽  
Pressure Jump ◽  
Interfacial Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Numerical Instabilities ◽  
Spurious Currents

A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.

Numerical Study of Thermosyphon Protection for Frost Heave

2015 ◽  
Author(s):  
Basel Abdalla ◽  
Chengye Fan ◽  
Colin McKinnon ◽  
Vincent Gaffard
Keyword(s):  
Numerical Study ◽  
Computational Cost ◽  
Rate Function ◽  
Frost Heave ◽  
Transient Temperature ◽  
Two Phase ◽  
Conduction Model ◽  
Element Analysis ◽  
Arctic Regions ◽  
Lens Growth

Thaw subsidence and frost heave are two different hazards to pipelines in arctic regions. The former is due to the thawing of permafrost induced by a warm pipeline, while the latter is resulted from a cold buried pipeline that causes ice lens growth upon freezing in the direction of heat loss. Some pipelines may be operated in a wide temperature range and thus subjected to both types of threats. Two-phase closed thermosyphons have been employed extensively in Arctic projects to protect the permafrost from thawing. The thermosyphons’ response as a “thermo-diode” is the key to this technology. This paper presents a finite element analysis (FEA) based feasibility study for using thermosyphons with pipelines in arctic regions to reduce the potential for frost heave. There are two major challenges in the numerical simulation. One is the efficient modeling of a thermosyphons which works as a heat pump in winter and stops working in summer. This study proposes an anisotropic conduction model that simplifies the thermal-fluid processes within the thermosyphon without overwhelming computational cost. The other challenge is the frost heave modeling, which was recently achieved based on the framework of the porosity rate function. New developments involved in this paper include the extended application to permafrost and transient temperature boundary conditions. The outcome of this work proves the value of using thermosyphons with pipelines that transfer both cold product. The method introduced here can also be used to optimize the design of new infrastructure and pipelines in permafrost, as well as to assess how thermosyphons work as a mitigation method in existing projects that are affected by frost heave.

A 3D strongly coupled implicit discontinuous Galerkin level set-based method for modeling two-phase flows

2013 ◽  
Vol 87 ◽  
pp. 144-155 ◽  
Author(s):  
François Pochet ◽  
Koen Hillewaert ◽  
Philippe Geuzaine ◽  
Jean-François Remacle ◽  
Émilie Marchandise
Keyword(s):  
Discontinuous Galerkin ◽  
Level Set ◽  
Two Phase Flows ◽  
Two Phase ◽  
Strongly Coupled

A numerical study of droplet splitting in branched T-shaped microchannel using the two-phase level-set method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110454
Author(s):  
Mohammad Raad ◽  
Sajad Rezazadeh ◽  
Habib Jalili ◽  
Davod Abbasinezhad Fallah
Keyword(s):  
Pressure Gradient ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Study ◽  
Immiscible Liquid ◽  
Length Ratio ◽  
Significant Feature ◽  
Two Phase ◽  
Droplet Splitting ◽  
Passive Technique

Droplet splitting as a significant feature of droplet-based microfluidic systems has been widely employed in biotechnology, biomedical engineering, tissue engineering, and it has been preferred over continuous flow systems. In the present paper, two-dimensional numerical simulations have been done to examine the asymmetrical droplet splitting process. The two-phase level set method (LSM) has been predicted to analyze the mechanism of droplet formation and droplet splitting in immiscible liquid/liquid two-phase flow in the branched T-junction microchannel. Governing equations on flow field have been discretized and solved using finite element-based COMSOL Multiphysics software (version 5.3a). Obtained numerical results were validated by experimental data reported in the literature which show acceptable agreement. The model was developed to simulate the mechanism of droplet splitting at the branched T-junction microchannel. This study provides a passive technique to asymmetrically split up microdroplets at the downstream T-junctions. The results show that outlet branches’ pressure gradient affects the droplet splitting. Specifically, it has been shown that the splitting ratio increases by increasing the length ratio, and equal droplet splitting can be achieved where the ratio is LL/ Lu = 1. We have used two outlet branches having the same width but different lengths to create the required pressure gradient. As the length ratio of the outlet branches increases, the diameter ratio increases as well.

Numerical Study of Primary Jet Breakup in a Simplex Swirl Atomizer Using Dual Grid Coupled Level Set VOF Method

2019 ◽  
Author(s):  
Krishna Kant ◽  
Mayank Kumar ◽  
Rajesh Reddy ◽  
Raja Banerjee ◽  
Narasimha Mangadoddy ◽  
...  
Keyword(s):  
Level Set ◽  
Numerical Study ◽  
Computational Cost ◽  
Pressure Profile ◽  
Vof Method ◽  
Grid Refinement ◽  
Level Set Function ◽  
Jet Breakup ◽  
Flow Features ◽  
Swirl Atomizer

Abstract Primary breakup of a liquid jet emanating from a simplex swirl atomizer is numerically studied in this work. The liquid-gas interface is tracked using a coupled Level-Set VOF method. In order to improve the curvature calculation, a dual grid approach is used. Level set function is solved on a grid that is finer than the grid used to solve the rest of the variables. This solver is developed using OpenFOAM libraries and is validated by estimating the pressure profile and spurious velocities across the interface of a static bubble. The validation test shows significant improvement in the performance of curvature estimation without significant increase in the computational cost. Additionally, it is found that curvature calculation improves with increase in grid refinement index. A parametric study to understand the effects of grid refinement index on the flow features of the simplex swirl atomizer primary jet is reported here.

Modeling of Internal and Near-Nozzle Flow for a GDI Fuel Injector

2015 ◽  
Author(s):  
Kaushik Saha ◽  
Sibendu Som ◽  
Michele Battistoni ◽  
Yanheng Li ◽  
S. Quan ◽  
...  
Keyword(s):  
Liquid Fuel ◽  
Numerical Study ◽  
Direct Injection ◽  
Computational Cost ◽  
Volume Averaging ◽  
Operating Conditions ◽  
Superheated Liquid ◽  
Fuel Injector ◽  
Two Phase ◽  
Flash Boiling

A numerical study of two-phase flow inside the nozzle holes and the issuing spray jets for a multi-hole direct injection gasoline injector has been presented in this work. The injector geometry is representative of the Spray G nozzle, an eight-hole counterbore injector, from the Engine Combustion Network (ECN). Simulations have been carried out for a fixed needle lift. Effects of turbulence, compressibility and non-condensable gases have been considered in this work. Standard k–ε turbulence model has been used to model the turbulence. Homogeneous Relaxation Model (HRM) coupled with Volume of Fluid (VOF) approach has been utilized to capture the phase change phenomena inside and outside the injector nozzle. Three different boundary conditions for the outlet domain have been imposed to examine non-flashing and evaporative, non-flashing and non-evaporative and flashing conditions. Noticeable hole-to-hole variations have been observed in terms of mass flow rates for all the holes under all the operating conditions considered in this study. Inside the nozzle holes mild cavitation-like and in the near-nozzle region flash boiling phenomena have been predicted when liquid fuel is subjected to superheated ambiance. Under favorable conditions considerable flashing has been observed in the near-nozzle regions. An enormous volume is occupied by the gasoline vapor, formed by the flash boiling of superheated liquid fuel. Large outlet domain connecting the exits of the holes and the pressure outlet boundary appeared to be necessary leading to substantial computational cost. Volume-averaging instead of mass-averaging is observed to be more effective, especially for finer mesh resolutions.

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