The aim of this series is to publish promptly and in a de- tailed form new material from the field of Numerical Fluid Mechanics including the use of advanced computer systems. Published are reports on specialized conferences, workshops, research programs, and monographs. Contents: This volume contains nineteen reports on work, which is conducted since 1998 in the Collaborative Research Programme "Numerical Flow Simulation" of the Centre National de la Recherche Scientifique (CNRS) and the Deutsche Forschungsgemeinschaft (DFG). French and German engineers and mathematicians present their joint research on the topics "Development of Solution Techniques", "Crystal Growth and Melts", "Flows of Reacting Gases", and "Turbulent Flows". In the background of their work is the still strong growth of the performance of super-computer architectures, which, together with large advances in algorithms, is opening vast new application areas of numerical flow simulation in research and industrial work. Results of this programme from the period 1996 to 1998 have been presented in NNFM 66 (1998).