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Exploration of Complexity in Flow Fields and Boundary Conditions for Analytical Solutions

This study investigates complexity in flow fields, boundary conditions, and coefficients for analytical solutions. The analysis includes uniform, tidal, spatial, and time-dependent flows with a focus on various flow characteristics and nonlinear coefficients. The study assesses the impact of uni-directional, bi-directional, linear decay, and stiff problems on flow behavior. Additionally, it explores the influence of remote and close boundary conditions on flow dynamics and reactions. The research considers both linear and nonlinear reactions, incorporating Gaussian mass distribution tests and analytical solution validations for different spatial and temporal variations in velocity, diffusivity, and permeability coefficients. The study aims to enhance understanding of flow complexities and boundary condition effects on analytical solutions. 8

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Exploration of Complexity in Flow Fields and Boundary Conditions for Analytical Solutions

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  1. Process Quiescent Uniform Tidal Spatial & Time Flow/Coeff. Flow Field 1-Complexity in Number of Process FIGURE KEY: 3. Uni-direction 11. Gaus. Plume 4. Bi- Direction Advect Disperse React A-D A-R A-D-R 5. Uni-direction 12. Sin Plume 6. Uni-direction 7. Remote BC 8. Close BC 9. Smooth Plume Nuemann 10. Smooth Plume Dirichlet 2-Complexity in Flow Field & Nonlinear Coefficients 1. Linear Decay 2. Stiff Problem 3-Complexity in BC 17. Spatial: V, A, & Ks 13. Remote BC Remote Boundary Condition (Trivial) 18. Temporal V, & Ks 14. Close BC 15. Liner Reaction Active Boundary Condition (Non-Trivial) 16. Sin Liner Reaction 21. Spatial and Temporal Variation in V, A, and Ks ,Nonlinear Source Term Other Analytical Solution Tests 19. Remote BC Gaussian Mass Distribution Tests 20. Close BC

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