Convergence Analysis of MCMC Methods for Subsurface Flow Problems

2018 ◽  
pp. 305-317
Author(s):  
Abdullah Mamun ◽  
Felipe Pereira ◽  
Arunasalam Rahunanthan
Keyword(s):  
Convergence Analysis ◽  
Subsurface Flow ◽  
Mcmc Methods ◽  
Flow Problems

scholarly journals Optimal Bayesian experimental design for subsurface flow problems

2020 ◽  
Vol 370 ◽  
pp. 113208
Author(s):  
Alexadner Tarakanov ◽  
Ahmed H. Elsheikh
Keyword(s):  
Experimental Design ◽  
Subsurface Flow ◽  
Flow Problems

scholarly journals A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing-En Xiao ◽  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Wei-Chung Yeih
Keyword(s):  
Free Surface ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Domain Decomposition Method ◽  
Subsurface Flow ◽  
Test Problems ◽  
Pressure Potential ◽  
Trefftz Method ◽  
Flow Problems ◽  
Boundary Type

A novel boundary-type meshless method for modeling geofluid flow in heterogeneous geological media was developed. The numerical solutions of geofluid flow are approximated by a set of particular solutions of the subsurface flow equation which are expressed in terms of sources located outside the domain of the problem. This pioneering study is based on the collocation Trefftz method and provides a promising solution which integrates the T-Trefftz method and F-Trefftz method. To deal with the subsurface flow problems of heterogeneous geological media, the domain decomposition method was adopted so that flux conservation and the continuity of pressure potential at the interface between two consecutive layers can be considered in the numerical model. The validity of the model is established for a number of test problems. Application examples of subsurface flow problems with free surface in homogenous and layered heterogeneous geological media were also carried out. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for solving subsurface flow with nonlinear free surface in layered heterogeneous geological media even with large contrasts in the hydraulic conductivity.

scholarly journals A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2595 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Weichung Yeih ◽  
Chia-Ming Fan
Keyword(s):  
Diffusion Equation ◽  
Meshless Method ◽  
Moving Boundary ◽  
Iterative Scheme ◽  
Separation Of Variables ◽  
Subsurface Flow ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Trefftz Method ◽  
Flow Problems

In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the superposition theorem using the basis functions, which match the data at the spacetime boundary collocation points. Because the proposed basis functions fully satisfy the diffusion equation, arbitrary nodes are collocated only on the spacetime boundaries for the discretization of the domain. The iterative scheme has to be used for solving the moving boundaries because the transient moving boundary problems exhibit nonlinear characteristics. Numerical examples, including harmonic and non-harmonic boundary conditions, are carried out to validate the method. Results illustrate that our method may acquire field solutions with high accuracy. It is also found that the method is advantageous for solving inverse problems as well. Finally, comparing with those obtained from the method of fundamental solutions, we may obtain the accurate location of the nonlinear moving boundary for transient problems using the spacetime meshless method with the iterative scheme.

scholarly journals Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

2020 ◽  
Vol 56 (5) ◽  
Author(s):  
A. M. Tartakovsky ◽  
C. Ortiz Marrero ◽  
Paris Perdikaris ◽  
G. D. Tartakovsky ◽  
D. Barajas‐Solano
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Subsurface Flow ◽  
Flow Problems ◽  
Constitutive Relationships
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