# l25 - Lecture 25 Introduction to Fluid Flow 1 Last Time...

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1 Lecture 25: Introduction to Fluid Flow

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2 Last Time… Examined physical rationale for limiter functions Applied to multidimensional situations and unstructured meshes This brings us to the end of the convection-diffusion part
3 This Time… Start looking at the computation of fluid flow Discuss issues with respect to sequential solution of continuity and momentum equations Discuss storage of pressure versus velocity

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4 Introduction to Fluid Flow So far, we have assumed that the fluid flow field is known We now turn to the computation of the fluid flow Navier-Stokes equations are special case of convection diffusion equation with = u, v or w, and = and appropriate S So why the fuss?
5 Steady 2D Navier-Stokes Equations Can write Navier-Stokes equations as: For Newtonian fluid, can confirm that:

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6 Why The Fuss? NS equations are non-linear » Not by itself a problem » Can do Picard iteration More than one momentum equation (x,y,z) » Not a problem » Can solve each sequentially Source terms? » Stress tensor sources can be computed Main issue is that pressure is not known! » Must find a way to find it » What PDE to use?
7 Issues with Pressure Computation Two different problems » Where to store pressure vis-à-vis velocity » How to find an equation for pressure In 3D, we have 4 equations in 4 unknowns » 3 velocities, 1 pressure » 3 momentum equations and one continuity equations In principle, possible to solve

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8 Vorticity-Stream Function Formulations Used during 70’s-80’s » Derive one PDE for stream function
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l25 - Lecture 25 Introduction to Fluid Flow 1 Last Time...

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