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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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Acceleration strategies for Tridimensional Coupled hydromechanical problems based on CPU and GPU programming in

Jean B Joseph1, Paulo Marcelo V Ribeiro1, Leonardo J N Guimarães1

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Novel computational strategies for reservoir geomechanics significantly accelerate fluid flow simulations in porous media. These methods leverage vectorized code on CPUs and GPUs, drastically reducing processing time and memory needs for complex geoscience applications.

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Area of Science:

  • Geophysics
  • Computational Science
  • Petroleum Engineering

Background:

  • Large-scale fluid flow in porous media is computationally intensive, impacting critical applications like groundwater management and oil recovery.
  • Reservoir geomechanics simulations require efficient numerical methods to handle complex physical processes.

Purpose of the Study:

  • To introduce novel computational strategies for enhancing the efficiency of reservoir geomechanics simulations.
  • To develop and compare vectorized CPU and GPU implementations for finite element matrix assembly and linear system solution.

Main Methods:

  • Finite element matrix assembly using explicit matrices and multidimensional products with vectorized MATLAB code.
  • Global sparse matrix assembly leveraging MATLAB's native sparse function.
  • Linear system solution employing the conjugate gradient solver (pcg) and the Eigen library on both CPU and GPU (using gpuArray and CUDA).

Main Results:

  • Demonstrated significant speedups in processing time compared to serial codes through vectorized CPU and GPU approaches.
  • Evaluated memory requirements for different computational strategies, highlighting efficiency gains.
  • Successful implementation of advanced computational techniques within the MATLAB environment.

Conclusions:

  • The proposed computational strategies offer substantial performance improvements for large-scale fluid flow simulations in porous media.
  • Vectorized CPU and GPU implementations provide efficient solutions for reservoir geomechanics problems.
  • These advances contribute to more feasible and rapid analysis in geoscience and engineering applications.