what exactly is the use of conservation form of the partial differential equations

(1). I think, it is a divergence form(vector operation) of the spatial variation part of the equation. (2). For steady-state equation, in divergence form, it can be translated into surface integral and represent the conservation law over the cell. (3). Conservation is only one property of the equation. Since the governing equations of fluid is a field equation, the information or disturbances can propagate in different ways throughout the field. (4). So, as a result, accurate solution of the equations does not just depend on the conservation law (or form), the Reynolds number, the Mach number, etc.. all have certain effects on the solution. (5). I normally write the equations in the expanded form in stead of the conservation form. It represents more accurately the order of the equations. On the other hand, the divergence form is first-order in appearance. In the expanded form, the equation is second-order partial differential equations.