179 1996 Rickard Enander, Björn Sjögreen rickard@tdb.uu.se Implicit Explicit Residual Smoothing for Upwind Schemes Abstract In this paper we will investigate if implicit residual smoothing can be used together with upwind discretizations when steady state solutions are computed. We will numerically examine the second order accurate Roe's method in different flow situations i two and three space dimensions. These experiments indicate that a significant amount of CPU-time can be saved by residual smoothing and especially the explicit version.