Summary A virtual‐characteristic approach is developed for thermo‐flow with finite‐volume methodology in which a multidimensional characteristic (MC) scheme is applied along with artificial compressibility. To obtain compatibility equations and pseudo‐characteristics, energy equation is taken into account in the MC scheme. With this inherent upwinding of convective fluxes, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of the MC scheme lies in its faster convergence rate with respect to the averaging scheme that is found to exhibit substantial delays in convergence. As benchmarks, forced and mixed convections in a cavity and in flow over cylinder and between parallel plates are examined for a wide range of Reynolds, Grashof, and Prandtl numbers. The MC and averaging schemes are applied for simulation purposes. Results show the better performance of the MC scheme in forced and mixed convections. Results confirm the robustness of the MC scheme in terms of accuracy and convergence. Copyright © 2015 John Wiley & Sons, Ltd.

A characteristic-based approach is developed for thermo-flow with finite volume methodology (FVM) in which multidimensional characteristic (MC) scheme is applied for convective fluxes. Artificial compressibility (AC) is used, and as a result governing equations take the hyperbolic nature. To obtain compatibility equations and pseudo characteristics, energy equation is taken into account in the MC scheme. With MC scheme for convective fluxes, no artificial viscosity is required even at high Reynolds numbers. As benchmarks, forced convection between parallel plates and forced and mixed convection in a cavity are examined for a wide range of Reynolds, Grashof and Prandtl numbers. First-order MC and second-order averaging schemes are used for simulate them. Results show the better performance of MC scheme in force convection as well as mixed convection. Results confirm the robustness of MC scheme in terms of accuracy and convergence, and are in good agreement with the standard benchmark solutions in the literature.

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