A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW W(3)
2015-12-08 01:08
导读：, dl denotes the arc length of the boundary , and n is a unit outward vector normal to the boundary . the vector u is assumed constant over an element. further discretizing (3), the basic equation of
, dl denotes the arc length of the boundary
, and n is a unit outward vector normal to the boundary
. 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
(6)or
(7)where
represents the angle between unit vector n and the x axis (along the counter-clockwise from the x axis),
and
denote transformation and inverse transformation matrices respectively
(8) eq. (4) can be rewritten as
(9) let the right terms of above equation be
, then
(10) two-step runge-kutta method is used to discretize eq. (10), then the second-order accuracy in time can be obtained
(11)the flux at every side of any element (e.g. at the side 1 of element
) can be given through the following form
(12)where
is the right eigenvector component (l=1,2,3) by roe's average state between the element
and the satellite element 1. a hybrid type form of
