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Welcome to the Convection-equation wiki! Test cases used is as follows:
Velocity = [(2x^{2} - x^{4})(y-y^{3}), -(2y^{2} - y^{4})(x-x^{3})]
RHS = 2(1 -x^2 + 1 - y^2)
Solution comes out to be (1 -x^2)(1 - y^2)