A new approach is described for numerically solving two-dimensional equations of radiation hydrodynamics. It has been specially developed for simulating heat exchange in combustion chambers, furnaces, and flames. It combines some features of u-v-p and Ψ-ω, zone and flux model solution methods while avoiding their shortcomings. A fine curvilinear orthogonal grid for computation of convection and a coarse zone grid for computation of radiation, as well as an effective procedure of intergrid interpolation, are used. A special feature of the method is that the Navier-Stokes finite-difference equations contain only the two variables u and v. Another feature is the choice of representative directions for propagation of thermal radiation and integration of the radiative transfer equations using a quick-sort algorithm. The method is fast acting, accurate, and applicable to complex geometry. Because the method retains the physics of the problem, complex mathematics are avoided.