Application of space-time method to steady flows

A finite volume method that uses the values of both the function and its spatial derivatives at all grid points is investigated. The additional unknowns are computed by using multiple control volumes per node. Discontinuities in the integrands are allowed inside the control volumes but not across the boundaries. Weak solutions are obtained by enforcing proper jump conditions on the resulting line integrals. Appropriate time-derivatives that ensure reliable and efficient convergence are identified by a combination of stability analyses and numerical experiment. Shock wave computations indicate the present method gives poorer solutions than does the companion time-accurate procedure. The discrepancy appears to be caused by the artificial dissipation used in the present results.