We consider a rotating vortex in gaseous flow in two space dimensions. The governing equations are the Euler equations for one polytropic gas. We construct a non-trivial radially symmetric and stationary solution by balancing hydrodynamic pressure and centripetal force per volume element, i.e.
where U(r) denotes the velocity at distance r away from the origin. For and the velocity fieldThis exact smooth solution is applicable to measure the accuracy of Cartesian finite volume schemes alone, but also to quantify the accuracy of imbedded boundary methods by constructing a radially symmetric no-slip boundary around the origin.
Configuration used in accuracy study for available patch solvers:
Velocity U(r) |
Pressure p(r) |
-- RalfDeiterding - 23 Feb 2005