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The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the…

Numerical Analysis · Mathematics 2024-09-18 Li Zhao , Chen-Song Zhang , Chun-Sheng Feng , Shi Shu

This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…

Computational Engineering, Finance, and Science · Computer Science 2017-01-24 Hui Liu , Lihua Shen , Yan Chen , Kun Wang , Bo Yang , Zhangxin Chen

We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…

Optimization and Control · Mathematics 2025-12-08 Radoslav Vuchkov , Eric C. Cyr , Aurya Javeed , Denis Ridzal

A parallel reservoir simulator has been developed, which is designed for large-scale black oil simulations. It handles three phases, including water, oil and gas, and three components, including water, oil and gas. This simulator can…

Computational Engineering, Finance, and Science · Computer Science 2016-10-10 Hui Liu , Lihua Shen , Kun Wang , Bo Yang , Zhangxin Chen

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was…

Numerical Analysis · Mathematics 2020-06-11 Matthias A. Cremon , Nicola Castelletto , Joshua A. White

OpenCAEPoro is a parallel numerical simulation software developed in C++ for simulating multiphase and multicomponent flows in porous media. The software utilizes a set of general-purpose compositional model equations, enabling it to handle…

Mathematical Software · Computer Science 2024-06-18 Shizhe Li , Chen-Song Zhang

In petroleum reservoir simulation, the industry standard preconditioner, the constrained pressure residual method (CPR), is a two-stage process which involves solving a restricted pressure system with Algebraic Multigrid (AMG). Initially…

Numerical Analysis · Mathematics 2019-06-19 Thomas Roy , Tom B. Jönsthövel , Christopher Lemon , Andrew J. Wathen

The fully implicit method is the most commonly used approach to solve black-oil problems in reservoir simulation. The method requires repeated linearization of large nonlinear systems and produces ill-condi\-tioned linear systems. We…

Numerical Analysis · Mathematics 2020-01-07 Øystein S. Klemetsdal , Atgeirr F. Rasmussen , Olav Møyner , Knut-Andreas Lie

As a competitive recovery method for heavy oil, In-Situ Combustion (ISC) shows its great potential accompanied by technological advances in recent years. Reservoir simulation will play an indispensable role in the prediction of the…

Computational Engineering, Finance, and Science · Computer Science 2018-11-30 Ruijian He , Bo Yang , Hui Liu , Zhangxin Chen

Growing heterogeneity and configurability in HPC architectures has made auto-tuning applications and runtime parameters on these systems very complex. Users are presented with a multitude of options to configure parameters. In addition to…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-04-28 Akash Dutta , Jordi Alcaraz , Ali TehraniJamsaz , Eduardo Cesar , Anna Sikora , Ali Jannesari

The ever-growing size of modern space-time data sets, such as those collected by remote sensing, requires new techniques for their efficient and automated processing, including gap-filling of missing values. CUDA-based parallelization on…

Computation · Statistics 2022-12-05 M. Lach , M. Žukovič

We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural…

Machine Learning · Computer Science 2019-09-23 Jiri Navratil , Alan King , Jesus Rios , Georgios Kollias , Ruben Torrado , Andres Codas

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…

Optimization and Control · Mathematics 2025-10-08 Emre Adabag , Marcus Greiff , John Subosits , Thomas Lew

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…

Computational Physics · Physics 2020-01-08 Lianhua Zhu , Peng Wang , Songze Chen , Zhaoli Guo , Yonghao Zhang

An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid…

Computational Physics · Physics 2018-08-07 Duane Rosenberg , Pablo D. Mininni , Raghu Reddy , Annick Pouquet

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…

Numerical Analysis · Mathematics 2018-01-26 Quan M. Bui , Howard C. Elman , J. D. Moulton

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

Numerical Analysis · Mathematics 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

Numerical Analysis · Mathematics 2013-02-18 Xiaozhe Hu , Shuhong Wu , Xiao-Hui Wu , Jinchao Xu , Chen-Song Zhang , Shiquan Zhang , Ludmil Zikatanov

For both isothermal and thermal petroleum reservoir simulation, the Constrained Pressure Residual (CPR) method is the industry-standard preconditioner. This method is a two-stage process involving the solution of a restricted pressure…

Numerical Analysis · Mathematics 2020-05-28 Thomas Roy , Tom B Jönsthövel , Christopher Lemon , Andrew J Wathen

The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…

Numerical Analysis · Mathematics 2026-04-13 Shizhe Li , Li Zhao , Chen-Song Zhang
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