A multidimensional chemistry coordinate mapping (CCM) approach is presented for efficient integration of chemical kinetics in numerical simulations of turbulent reactive flows. In CCM the flow transport is integrated in the computational cells in physical space, whereas the integration chemical reactions are carried out in a phase space made up of a few principal variables. Each cell in the phase space corresponds to several computational cells in the physical space, resulting in a speedup of the numerical integration. In reactive flows with small hydrocarbon fuels two principal variables have been shown to be satisfactory to construct the phase space. The two principal variables are the temperature (T) and the specific element mass ratio of the H atom (J _H). A third principal variable, σ=∇J _H·∇J _H, which is related to the dissipation rate of J _H, is required to construct the phase space for combustion processes with an initially non-premixed mixture. For complex higher hydrocarbon fuels, e.g. n-heptane, care has to be taken in selecting the phase space in order to model the low-temperature chemistry and ignition process. In this article, a multidimensional CCM algorithm is described for a systematic selection of the principal variables. The method is evaluated by simulating a laminar partially remixed pre-vaporised n-heptane jet ignition process. The CCM approach is then extended to simulate n-heptane spray combustion by coupling the CCM and Reynolds averaged Navier–Stokes (RANS) code. It is shown that the computational time for the integration of chemical reactions can be reduced to only 3–7%, while the result from the CCM method is identical to that of direct integration of the chemistry in the computational cells.