.

    The vector U is assumed constant over an element. Further discretizing (3), the basic equation of the finite volume method can be obtained

                                               (4)

where  is the length of side k,  denotes the outer normal flux vector of side k.  satisfies                                     

                                              (5)

   F(U) and G(U) have a rotational invariance property, so they satisfy the relation

        &

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