A simple augmented IIM for 3D incompressible two-phase Stokes flows with interfaces and singular forces

Wang, Weiyi; Tan, Zhijun

doi:10.1016/j.cpc.2021.108154

Cited by 7 publications

(15 citation statements)

References 45 publications

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“…Let us remark on the choice of test examples in the following. As mentioned earlier, we aim to emphasize the ease of implementation for the problem compared with the traditional IIM; thus, we have taken the test examples in 2D and 3D directly from the literature [10] and [24], respectively. One might wonder why the interfaces Γ chosen there are in circular (2D) or spherical (3D) form.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Table 4 shows the results for different (N p , N u ) values. One can see that using far less learnable parameters (maximal N θ = 1200 parameters to be learned) and training points (M = 6216), we are able to produce accurate results comparable to the augmented IIM proposed in [24].…”

mentioning

confidence: 82%

“…Again, the interfacial force can be derived from the jump condition (9) as [24] with grid resolutions 64 3 , 128 3 , and 256 3 .…”

Section: Presentmentioning

confidence: 99%

“…Example 4: As the fourth example (also referred to as Example 6.3 in [24]), we keep the domain Ω and interface Γ the same as shown in Example 3. The piecewise constant viscosity is also chosen as µ − = 1 and µ + = 0.1.…”

Section: Presentmentioning

confidence: 99%

See 3 more Smart Citations

A Cusp-Capturing Pinn for Elliptic Interface Problems

Tseng

Lin

et al. 2022

SSRN Journal

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Section: Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 82%

“…Again, the interfacial force can be derived from the jump condition (9) as [24] with grid resolutions 64 3 , 128 3 , and 256 3 .…”

Section: Presentmentioning

confidence: 99%

Section: Presentmentioning

confidence: 99%

See 2 more Smart Citations

A Cusp-Capturing Pinn for Elliptic Interface Problems

Tseng

Lin

et al. 2022

SSRN Journal

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“…As a result, the GMRES iterative method is used to solve the Schur complement system for the augmented variable jumps. Recently, Wang et al [24] used the similar idea but a simple version of IIM and extended the method to solve the three-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

A Discontinuity and Cusp Capturing PINN for Stokes Interface Problems with Discontinuous Viscosity and Singular Forces

null,

Lai

2023

AAM

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In this paper, we present a discontinuity and cusp capturing physicsinformed neural network (PINN) to solve Stokes equations with a piecewiseconstant viscosity and singular force along an interface. We first reformulate the governing equations in each fluid domain separately and replace the singular force effect with the traction balance equation between solutions in two sides along the interface. Since the pressure is discontinuous and the velocity has discontinuous derivatives across the interface, we hereby use a network consisting of two fully-connected sub-networks that approximate the pressure and velocity, respectively. The two sub-networks share the same primary coordinate input arguments but with different augmented feature inputs. These two augmented inputs provide the interface information, so we assume that a level set function is given and its zero level set indicates the position of the interface. The pressure sub-network uses an indicator function as an augmented input to capture the function discontinuity, while the velocity sub-network uses a cusp-enforced level set function to capture the derivative discontinuities via the traction balance equation. We perform a series of numerical experiments to solve two-and three-dimensional Stokes interface problems and perform an accuracy comparison with the augmented immersed interface methods in literature. Our results indicate that even a shallow network with a moderate number of neurons and

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Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems

Hua

Zhao

et al. 2023

J Sci Comput

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A simple augmented IIM for 3D incompressible two-phase Stokes flows with interfaces and singular forces

Cited by 7 publications

References 45 publications

A Cusp-Capturing Pinn for Elliptic Interface Problems

A Cusp-Capturing Pinn for Elliptic Interface Problems

A Discontinuity and Cusp Capturing PINN for Stokes Interface Problems with Discontinuous Viscosity and Singular Forces

Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems

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