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This study introduces a novel numerical simulation method for coupled diffusion, advection, and linear transport phenomena. The approach effectively manages complex geometries, ensuring computation time is independent of geometric detail.

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Area of Science:

  • Computational physics
  • Numerical methods
  • Scientific computing

Background:

  • Simulating coupled physical phenomena like diffusion, advection, and linear transport presents challenges, particularly with complex geometries.
  • Existing numerical methods can struggle with computational cost as geometric complexity increases.
  • Advances in computer graphics offer potential solutions for handling complex scenes efficiently.

Purpose of the Study:

  • To develop a numerical simulation technique for the coupling of diffusion, advection, and one-speed linear transport.
  • To demonstrate insensitivity to geometric complexity in these coupled phenomena.
  • To facilitate engineering calculations in complex geometrical environments.

Main Methods:

  • Adapting Monte Carlo algorithms from computer graphics for simulating coupled physical phenomena.
  • Replacing pure linear transport paths with advection-diffusion/linear-transport paths composed of subpaths.
  • Handling coupling by switching between subpaths representing diffusion, advection, and linear transport.

Main Results:

  • Achieved numerical simulation of coupled diffusion, advection, and one-speed linear transport.
  • Demonstrated that computation time is independent of geometric complexity, even with up to 10,000 pores.
  • Validated the approach in a porous medium simulation.

Conclusions:

  • The developed method effectively simulates coupled physical phenomena in complex geometries.
  • This approach offers significant engineering flexibility by decoupling computational cost from geometric detail.
  • The technique is applicable to various fields requiring simulation of transport phenomena in intricate environments.