A detailed investigation is presented to simulate the reactive flow field in a low-pressure flow reactor for kinetic studies. This has been done to improve existing methods for evaluating data from isothermal flow kinetic measurements. The full Navier-Stokes equations for compressible flows including transport phenomena and chemical reactions have been solved numerically for the low Mach number case. By using splitting techniques for variables and spatial dimensions, the calculation time could be reduced by more than 2 orders of magnitude. This reduction allows the repeated application of the solver to adjust parameters in the kinetic model organized as an optimization problem and give best agreement between experiment and calculation. The model results for the nonreactive flow field have been verified by comparison to imaging measurements via two-dimensional laser-induced fluorescence of acetone tracer gases for the visualization of diffusive mixing. Numerical results of full reactive flow simulation have been compared with the measurement of elementary relaxation processes and vibrational energy transfer in collisions of vibrationally excited hydrogen and deuterium molecules. Spatially resolved axial and radial concentration profiles of both species were obtained at room temperature using coherent anti-Stokes Raman spectroscopy (CARS). From the detailed numerical simulation evaluated wall deactivation probabilities at 300 K for H-2(v=1) --> (wall) H-2(v=0) (Ia) of gamma(w) = (1.5 +/- 0.3) x 10(-3) s and thermal rate constants for vibrational energy transfer H-2(v=1) + D-2(v=0) --> H-2(v=0) + D-2(v=1) (IIa) of k(vv) = (6 +/- 0.5) x 10(9) cm(3) mol(-1) s(-1) were derived using an optimization procedure specially adapted to the present kinetic problem. They are larger, respectively, by a factor of 2 (wall deactivation) and 1.4 (vibrational energy transfer) compared with values obtained from a plug-flow evaluation. While the k(vv) data from different experiments are now in excellent agreement, theoretical results using recent ab initio potentials still differ by a factor of 2.