An image-incorporated immersed boundary method for diffusion equations

by   Andrew C. Chiang, et al.

A novel sharp interface ghost-cell based immersed boundary method has been proposed and its parameters have been optimized against an analytical model in diffusion applications. The proposed embedded constrained moving least-squares (ECMLS) algorithm minimizes the error of the interpolated concentration at the image point of the ghost point by applying a moving least-squares method on all internal nodes, near the ghost image point, and the associated mirrored image points of these internal nodes through the corresponding boundary conditions. Using an analytical model as a reference, the ECMLS algorithm is compared to the constrained moving least-squares (CMLS) algorithm and the staircase model using various grid sizes, interpolation basis functions, weight functions, and the penalty parameter of the constraint. It is found that using ECMLS algorithm in the investigated diffusion application, the incomplete quartic basis function yields the best performance while the quadratic, cubic, and bicubic basis functions also produce results better than the staircase model. It is also found that the linear and bilinear basis functions cannot produce results better than the staircase model in diffusion applications. It is shown that the optimal radius of the region of internal nodes used for interpolation scales with the logarithm of the boundary radius of curvature. It is shown that for the diffusion application, the proposed ECMLS algorithm produces lower errors at the boundary with better numerical stability over a wider range of basis functions, weight functions, boundary radius of curvature, and the penalty parameter than the CMLS algorithm.



There are no comments yet.


page 15

page 19

page 20

page 21

page 24


Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients

We introduce a new numerical method based on machine learning to approxi...

An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces

We explore a new way to handle flux boundary conditions imposed on level...

Transfer Function Models for Particle Diffusion in a Horizontal Cylindrical Shape with a Vertical Force Component

This paper considers particle propagation in a cylindrical molecular com...

On immersed boundary kernel functions: a constrained quadratic minimization perspective

In the immersed boundary (IB) approach to fluid-structure interaction mo...

Unification of variational multiscale analysis and Nitsche's method, and a resulting boundary layer fine-scale model

We show that in the variational multiscale framework, the weak enforceme...

Modeling moving boundary value problems in electrochemical machining

This work presents a new approach to efficiently model the cathode in th...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.