Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method
In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layere...
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doaj-bc39e7bbdf4c4984bf8658689afb9fe12021-04-11T23:00:38ZengMDPI AGApplied Sciences2076-34172021-04-01113421342110.3390/app11083421Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz MethodCheng-Yu Ku0Li-Dan Hong1Chih-Yu Liu2Jing-En Xiao3Wei-Po Huang4School of Engineering, National Taiwan Ocean University, Keelung 20224, TaiwanSchool of Engineering, National Taiwan Ocean University, Keelung 20224, TaiwanSchool of Engineering, National Taiwan Ocean University, Keelung 20224, TaiwanSchool of Engineering, National Taiwan Ocean University, Keelung 20224, TaiwanSchool of Engineering, National Taiwan Ocean University, Keelung 20224, TaiwanIn this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.https://www.mdpi.com/2076-3417/11/8/3421Trefftz methodspace–time collocationlayered porous mediameshless methodtransient |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu Jing-En Xiao Wei-Po Huang |
spellingShingle |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu Jing-En Xiao Wei-Po Huang Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method Applied Sciences Trefftz method space–time collocation layered porous media meshless method transient |
author_facet |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu Jing-En Xiao Wei-Po Huang |
author_sort |
Cheng-Yu Ku |
title |
Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method |
title_short |
Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method |
title_full |
Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method |
title_fullStr |
Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method |
title_full_unstemmed |
Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method |
title_sort |
modeling transient flows in heterogeneous layered porous media using the space–time trefftz method |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2021-04-01 |
description |
In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided. |
topic |
Trefftz method space–time collocation layered porous media meshless method transient |
url |
https://www.mdpi.com/2076-3417/11/8/3421 |
work_keys_str_mv |
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