Developing an Integral Equation Solution for the Incompressible Navier-Stokes Equations
JSHS · 2020
Overview
Mrs. Jessica Williams Dr. Leonard Gray Computational modeling of viscous fluids has numerous industrial applications, and improving upon current fluid models, especially those for nonlinear fluids, while reducing computation time is of great interest. This project develops an algorithm to compute the "body force" volume integral derived from a Stokes boundary integral formulation of a general 3D axisymmetric fluid. To do so, the axi-symmetric volume integral is reformulated as the sum of a boundary integral and remainder volume integral, and a Galerkin approximation is then implemented for the integral equations. Simple numerical tests are used to verify the algorithm for the nonhomogeneous axi- symmetric Stokes equations.
Competition history
- JSHS 2020
Resources
Related projects
ISEF · 2019
Applied Mathematical Modeling of Continuous Dynamic Systems of Fluids in Pipe Flows
ISEF · 2026
Energy-Stable Numerical Method for Blood Flow in 3D Brain Aneurysms
ISEF · 2020
Consideration of Non-Constant Viscosity in the Analysis of the Navier-Stokes Equations
JSHS · 2025
Revolutionizing Turbulence Studies: Novel Low-Cost Zero Mean-Flow Chamber Design and Physics-Informed Tensor Basis Neural Network
ISEF · 2025
A Novel Low-Cost Zero Mean-Flow Chamber Design and Physics-Informed Neural Network for Astrophysical and Environmental Turbulence Applications
ISEF · 2019
An Optimized Multigrid Algorithm for Enabling Efficient Physical Simulations on Realistic Geometries
ISEF · 2018
Dynamics of the Flows with Moving Contact Line
ISEF · 2026
On Scale Dependent Velocity Fluctuations Generated by Molecular Collisions in Coarse-Grained Fluid Motion as a First Principles Basis for Stochastic Hydrodynamics and Their Implications for Navier-Stokes Smoothness Through Scale Time Limitations of Continuum Averaging
Closest projects by meaning, across every fair and year in the corpus.