PART B Consider advection only transport equation in one dimension: at +u-= = 0 Ox (2)...

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PART B Consider advection only transport equation in one dimension: at +u-= = 0 Ox (2) (a) Write the Finite Difference Approximation (FDA) of Equation (2) using forward differences in time and upwind differences in space (u < 0) for the advection term using explicit formulation. [5 Marks] (b) Apply Von Neumann stability analysis to FDA written in (a). [15 Marks] (c) Is the scheme unstable, stable or unconditionally stable? Give reasons for your answer based on your analysis in (b) and specify the stability criterion. [5 Marks] PART B Consider advection only transport equation in one dimension: at +u-= = 0 Ox (2) (a) Write the Finite Difference Approximation (FDA) of Equation (2) using forward differences in time and upwind differences in space (u < 0) for the advection term using explicit formulation. [5 Marks] (b) Apply Von Neumann stability analysis to FDA written in (a). [15 Marks] (c) Is the scheme unstable, stable or unconditionally stable? Give reasons for your answer based on your analysis in (b) and specify the stability criterion. [5 Marks]