A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations

Hsu, Shih Hsuan; Hu, Wen‐Chen; Lai, Ming Chih

doi:10.1016/j.jcp.2019.108903

Cited by 9 publications

(8 citation statements)

References 29 publications

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“…Although the present network is similar in spirit to PINNs [9], here we only use one hidden layer with sufficiently small number of neurons so it reduces the computational complexity and learning workload significantly without sacrificing the accuracy. Moreover, as shown in some examples in next section, the present DCSNN not only achieves better accuracy than the traditional finite difference method such as immersed interface method [15,18,19] in solving Eq. ( 8) but also outperforms other piecewise DNN [14] in terms of accuracy and network complexity.…”

Section: Elliptic Interface Problemsmentioning

confidence: 74%

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A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

Lin

Lai

2021

Preprint

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In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating d-dimensional piecewise continuous functions and for solving elliptic interface problems is developed. There are three novel features in the present network; namely, (i) jump discontinuity is captured sharply, (ii) it is completely shallow consisting of only one hidden layer, (iii) it is completely mesh-free for solving partial differential equations (PDEs). We first continuously extend the d-dimensional piecewise continuous function in (d + 1)-dimensional space by augmenting one coordinate variable to label the pieces of discontinuous function, and then construct a shallow neural network to express this new augmented function. Since only one hidden layer is employed, the number of training parameters (weights and biases) scales linearly with the dimension and the neurons used in the hidden layer. For solving elliptic interface equations, the network is trained by minimizing the mean squared error loss that consists of the residual of governing equation, boundary condition, and the interface jump conditions. We perform a series of numerical tests to compare the accuracy and efficiency of the present network. Our DCSNN model is comparably efficient due to only moderate number of parameters needed to be trained (a few hundreds of parameters used throughout all numerical examples here), and the result shows better accuracy (and less parameters) than other method using piecewise deep neural network in literature. We also compare the results obtained by the traditional grid-based immersed interface method (IIM) which is designed particularly for elliptic interface problems. Again, the present results show better accuracy than the ones obtained by IIM. We conclude by solving a six-dimensional problem to show the capability of the present network for high-dimensional applications.

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Section: Elliptic Interface Problemsmentioning

confidence: 74%

“…We then compare the accuracy of the DCSNN solution with the 3D immersed interface solver proposed in [19]. Note that, in 3D IIM, the total degree of freedom, N deg , is now the sum of the number of Cartesian grid points m 3 and the augmented projection foots on the interface, m Γ .…”

Section: Numerical Resultsmentioning

confidence: 99%

A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

Lin

Lai

2021

Preprint

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“…On the computational side, several simulation studies have solved the Melcher–Taylor leaky-dielectric model using boundary integral methods (Sherwood 1988; Lac & Homsy 2007; Lanauze, Walker & Khair 2015; Nganguia et al. 2016; Das & Saintillan 2017 a ) or grid-based methods (López-Herrera, Popinet & Herrada 2011; Hsu, Hu & Lai 2019; Theillard, Gibou & Saintillan 2019) and often match well with experiments (Ha & Yang 2000 a , b ; Salipante & Vlahovska 2010). It is also worth mentioning a related problem concerning the behaviour and breakup of conducting drops in electric fields (Dubash & Mestel 2007 a , b ; Karyappa, Deshmukh & Thaokar 2014).…”

Section: Introductionmentioning

confidence: 99%

“…Since his pioneering work, there have been several attempts to include various effects such as transient shape deformations (Esmaeeli & Sharifi 2011), transient charge relaxation and fluid acceleration (Lanauze, Walker & Khair 2013), or coupling with other fields such as gravity (Bandopadhyay et al 2016;Yariv & Almog 2016). On the computational side, several simulation studies have solved the Melcher-Taylor leaky-dielectric model using boundary integral methods (Sherwood 1988;Lac & Homsy 2007;Lanauze, Walker & Khair 2015;Nganguia et al 2016;Das & Saintillan 2017a) or grid-based methods (López-Herrera, Popinet & Herrada 2011;Hsu, Hu & Lai 2019;Theillard, Gibou & Saintillan 2019) and often match well with experiments (Ha & Yang 2000a,b;Salipante & Vlahovska 2010). It is also worth mentioning a related problem concerning the behaviour and breakup of conducting drops in electric fields (Dubash & Mestel 2007a,b;Karyappa, Deshmukh & Thaokar 2014).…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional small-deformation theory for electrohydrodynamics of dielectric drops

Das

Saintillan

2021

J. Fluid Mech.

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“…Since his pioneering work, there have been several attempts to include various effects such as transient shape deformations (Esmaeeli 914 A22-2 Three-dimensional electrohydrodynamic drop theory & Sharifi 2011), transient charge relaxation and fluid acceleration (Lanauze, Walker & Khair 2013), or coupling with other fields such as gravity (Bandopadhyay et al 2016;Yariv & Almog 2016). On the computational side, several simulation studies have solved the Melcher-Taylor leaky-dielectric model using boundary integral methods (Sherwood 1988;Lac & Homsy 2007;Lanauze, Walker & Khair 2015;Nganguia et al 2016;Das & Saintillan 2017a) or grid-based methods (López-Herrera, Popinet & Herrada 2011;Hsu, Hu & Lai 2019;Theillard, Gibou & Saintillan 2019) and often match well with experiments (Ha & Yang 2000a,b;Salipante & Vlahovska 2010). It is also worth mentioning a related problem concerning the behaviour and breakup of conducting drops in electric fields (Dubash & Mestel 2007a,b;Karyappa, Deshmukh & Thaokar 2014).…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional small-deformation theory for electrohydrodynamics of dielectric drops

Das

2021

Preprint

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Electrohydrodynamics of drops is a classic fluid mechanical problem where deformations and microscale flows are generated by application of an external electric field. In weak fields, electric stresses acting on the drop surface drive quadrupolar flows inside and outside and cause the drop to adopt a steady axisymmetric shape. This phenomenon is best explained by the leaky-dielectric model under the premise that a net surface charge is present at the interface while the bulk fluids are electroneutral. In the case of dielectric drops, increasing the electric field beyond a critical value can cause the drop to start rotating spontaneously and assume a steady tilted shape. This symmetry-breaking phenomenon, called Quincke rotation, arises due to the action of the interfacial electric torque countering the viscous torque on the drop, giving rise to steady rotation in sufficiently strong fields. Here, we present a small-deformation theory for the electrohydrodynamics of dielectric drops for the complete Melcher-Taylor leaky-dielectric model in three dimensions. Our theory is valid in the limits of strong capillary forces and highly viscous drops and is able to capture the transition to Quincke rotation. A coupled set of nonlinear ordinary differential equations for the induced dipole moments and shape functions are derived whose solution matches well with experimental results in the appropriate small-deformation regime. Retention of both the straining and rotational components of the flow in the governing equation for charge transport enables us to perform a linear stability analysis and derive a criterion for the applied electric field strength that must be overcome for the onset of Quincke rotation of a viscous drop.

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A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations

Cited by 9 publications

References 29 publications

A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems

A three-dimensional small-deformation theory for electrohydrodynamics of dielectric drops

A three-dimensional small-deformation theory for electrohydrodynamics of dielectric drops

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