Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method
This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equati...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-12-01
|
Series: | Water |
Subjects: | |
Online Access: | https://www.mdpi.com/2073-4441/12/12/3580 |
id |
doaj-01396b8d10dc4336bd053fbb78c84ec8 |
---|---|
record_format |
Article |
spelling |
doaj-01396b8d10dc4336bd053fbb78c84ec82020-12-21T00:01:14ZengMDPI AGWater2073-44412020-12-01123580358010.3390/w12123580Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz MethodCheng-Yu Ku0Li-Dan Hong1Chih-Yu Liu2School 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, TaiwanThis paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to validate the proposed approach. Emphasis is placed on the two-dimensional boundary detection problem in which the nonlinearity is solved using the fictitious time integration method. Results demonstrate that approximations with high accuracy are acquired in which the boundary data on the absent boundary may be efficiently recovered even when inaccessible partial data are provided.https://www.mdpi.com/2073-4441/12/12/3580Trefftz basis functionsinverse problemsboundary detection problemstransientmeshfree method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu |
spellingShingle |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method Water Trefftz basis functions inverse problems boundary detection problems transient meshfree method |
author_facet |
Cheng-Yu Ku Li-Dan Hong Chih-Yu Liu |
author_sort |
Cheng-Yu Ku |
title |
Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method |
title_short |
Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method |
title_full |
Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method |
title_fullStr |
Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method |
title_full_unstemmed |
Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method |
title_sort |
solving transient groundwater inverse problems using space–time collocation trefftz method |
publisher |
MDPI AG |
series |
Water |
issn |
2073-4441 |
publishDate |
2020-12-01 |
description |
This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to validate the proposed approach. Emphasis is placed on the two-dimensional boundary detection problem in which the nonlinearity is solved using the fictitious time integration method. Results demonstrate that approximations with high accuracy are acquired in which the boundary data on the absent boundary may be efficiently recovered even when inaccessible partial data are provided. |
topic |
Trefftz basis functions inverse problems boundary detection problems transient meshfree method |
url |
https://www.mdpi.com/2073-4441/12/12/3580 |
work_keys_str_mv |
AT chengyuku solvingtransientgroundwaterinverseproblemsusingspacetimecollocationtrefftzmethod AT lidanhong solvingtransientgroundwaterinverseproblemsusingspacetimecollocationtrefftzmethod AT chihyuliu solvingtransientgroundwaterinverseproblemsusingspacetimecollocationtrefftzmethod |
_version_ |
1724375990769025024 |