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Related Concept Videos

Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
Accelerating Fluids01:17

Accelerating Fluids

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.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:

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A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
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A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

George S H Pau1, Ann S Almgren, John B Bell

  • 1Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. gpau@lbl.gov

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 21, 2009
PubMed
Summary

This study introduces an adaptive algorithm for simulating multi-phase, incompressible flow in porous media. The method ensures accuracy and efficiency through simultaneous space-time grid refinement for complex fluid dynamics.

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Microfluidic Devices for Characterizing Pore-scale Event Processes in Porous Media for Oil Recovery Applications
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Microfluidic Devices for Characterizing Pore-scale Event Processes in Porous Media for Oil Recovery Applications

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Area of Science:

  • Computational fluid dynamics
  • Porous media flow
  • Numerical analysis

Background:

  • Darcy's law governs fluid flow in porous media, often involving multiple phases.
  • Accurate simulation of multi-phase flow requires robust numerical methods.
  • Adaptive algorithms enhance computational efficiency by refining grids where needed.

Purpose of the Study:

  • To develop a second-order accurate adaptive algorithm for multi-phase, incompressible flow in porous media.
  • To implement a nested hierarchy of grids with simultaneous space-time refinement.
  • To demonstrate the algorithm's accuracy and convergence properties.

Main Methods:

  • Utilized a multi-phase Darcy's law with relative permeabilities dependent on phase saturation.
  • Employed a total-velocity splitting approach to solve a second-order elliptic pressure equation.
  • Recasted component conservation equations as nonlinear hyperbolic equations for adaptive refinement.
  • Implemented a recursive integration procedure on a hierarchy of grids with synchronized data across levels.

Main Results:

  • Presented a second-order accurate adaptive algorithm for multi-phase, incompressible flow.
  • Demonstrated the algorithm's accuracy and convergence properties through numerical examples.
  • Illustrated the behavior of the adaptive space-time refinement method.

Conclusions:

  • The developed adaptive algorithm effectively simulates multi-phase, incompressible flow in porous media.
  • The simultaneous space-time grid refinement strategy enhances computational efficiency and accuracy.
  • The method provides a robust framework for analyzing complex fluid dynamics in porous media.