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in order to define the navier stokes equation in the mathematical description of fluid flow, it is necessary to assume that velocity and pressure vary continuously from one point to another. We may describe these properties with continuous functions of space and time and may apply differential equations in the analysis of processes. Equations derived on the basis of this assumption have withstood the test of time and the consideration of a fluid medium as a continuum has firmly been established.
we can establish these equation if we assume the equation are derivative to a second order to be able to linearise the equation
Depends on what you are doing with the discontinuum- is it a part of your computational domain ? If it is, do you know its exact position ? If you do, decide how the prisms or gap elements have to be inserted there. Otherwise, the significance depends on how significant is the discontinuity and accordingly we choose various algorithms that give us the desired result (eg:- turbulence models...in case u r more concerned to find out the location of a lambda shock in the B.L.)
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