A Study of Flow in a Corrugated Channel Xin Kai Li Institute of Simulation Sciences De Montfort University Leicester UK.

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A Study of Flow in a Corrugated Channel Xin Kai Li Institute of Simulation Sciences De Montfort University Leicester UK

Outline Introduction Mathematical model Spectral element method for a corrugated channel flow Numerical results Conclusion with further work

Mathematical Model Momentum equation Mass equation Constitutive Equation

Viscosity model Cross model

Spectral Element method Gauss-Lobatto-Legendre Polynomials

Basis functions (Gauss-Lobatto-Legendre polynomials) for the velocity and the extra-stress tensor Basis function for the pressure and the deformation tensor

Spectral element configuration (k=4, M=N=5) Gauss-Lobatto-Legendre collocation points for the velocity and stress tensor Interior Gauss-Lobatto-Legendre collocation points for the pressure p ( u,  )

Numerical algebraic equations A ---- Helmholtz operator B ---- Gradient operator C ---- Stress tensor matrix

Numerical example Flow geometry

Velocity profiles

Shear rate and viscosity

Velocity vector profiles

Velocity along the x-axis