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In this work, an efficient bi-implicit strategy is suitably developed within the context of a hybrid finite volume element method to solve axisymmetric turbulent reactive flow in a model gas turbine combustor. Based on the essence of a control-volume-based finite-element method, the formulation benefits from the geometrical flexibility of the finite element methods while the discrete algebraic governing equations are derived through applying the conservation laws to discrete cells distributed in the solution domain. To enhance the efficiency of method, we extend the physical influence upwinding scheme to cylindrical coordinates. This extension helps to improve the advection flux... 

In this work, the conservation forms of the reacting ow governing equations are treated mainly using a cell-centered finite-volume approach with a collocated storage of all trans- port variables. However, the finite volume formulations are suitably incorporated with the finite element expressions. As an innovation, a physical influence upwinding scheme is suitably extended to the cylindrical coordinate system to approximate the convective terms of the governing conservation laws at the cell faces. This treatment firstly respects the physics of flow and secondly provides the necessary coupling of velocity and pressure fields in this frame. The numerical solution of laminar, buoyant difiusion...