Steady Convection: Discretization Schemes and TVD Methods

This lecture covers discretization schemes for the convective term, including upwind differencing (UD), central differencing (CD), and higher-order schemes like LUD and QUICK. It also introduces Total Variation Diminishing (TVD) methods, which aim to achieve higher-order accuracy without introducing new extrema. The instructor explains the criteria for boundedness and 2nd-order accuracy in TVD schemes, along with various limiter functions such as Van Leer, Van Albada, and SUPERBEE. Practical examples and guidelines are provided, highlighting the advantages of TVD schemes in numerical flow simulations over traditional methods like UD and CD.