We describe the low Mach variable-density Navier-Stokes numerical iterative solution procedure implemented in the finite-volume unstructured T-FlowS code. As the test cases we use a number of analytic manufactured solutions and Rayleigh-Taylor instability problem from the literature for algorithm verification purposes. The tests show that the code is second-order accurate in agreement with the spatial discretization scheme. We outline the recent combustion ADEF model implemented in the program.@en