离心泵特性曲线-scalar.pdf

4. THE SCALAR TRANSPORT EQUATION SPRING 2005 4.1 The finite-volume method 4.2 The one-dimensional advection-diffusion equation 4.3 Classroom examples 4.4 Discretising diffusion 4.5 Discretising the source term 4.6 Assembling the algebraic equations 4.7 Extension to 2 and 3 dimensions 4.8 Advection schemes (part I) 4.9 Discretisation properties 4.10 Constraints on the matrix coefficients 4.11 Advection schemes (part II) 4.12 Implementation of higher-order advection schemes 4.13 Curvilinear meshes 4.14 Boundary conditions 4.15 Solution of the algebraic equations 4.16 Summary Appendix: Tri-diagonal matrix algorithm For a conserved physical quantity and an arbitrary control volume, rate of change within control volume + net outwardf lux = source within cell (1) The total flux through a surface consists of advection (movement with the flow) u and diff usion (net transport by random molecular or turbulent fluctuations). If φ is V un the amount of the conserved quantity per unit mass of fluid, then the generic A scalar-transp ort (or advection-diff usion) equation may be written: d ∂φ ( Vφ) + ( Cφ − A ) = S V dt f aces ∂n (2) rate of change advection diff usion source Thef inite-volume method is a discretisation of (2). This Section focuses on steady flow. 4.1 The Finite-Volume Method (1) A flow geometry is defined. (2) The flow domain is decomposed into a comp utational mesh or grid – a set of non-overlapping control volumes or cells – over which the integral equations are to be discretised. (