A low-dissipation continuous Galerkin formulation for turbulent premixed combustion

• Propose a low-dissipative method for solving advection-dominated problems based on combining the streamline-upwind Petrov-Galerkin (SUPG) approach with the entropy viscosity stabilization method. • Introduce a novel approach to approximate the time derivative in the entropy inequality. • Highlight the necessity of avoiding over-undershoots in the scalar transport equation, crucial for solving reacting flows with tabulated chemistry. • Significantly suppresses the magnitude of numerical over-undershoots and minimizes associated errors, while acknowledging that complete elimination is not strictly guaranteed. • Reveal the importance of using a low-dissipative method for the scalar transport equation in a premixed turbulent combustion case. This work presents a low-dissipative numerical method to solve the scalar transport equation with an exhaustive analysis of its application to reacting flows in the limit of perfectly premixed combustion with a low-Mach number formulation. A tabulated flamelet model is used to simplify the chemical reactions. The proposed method is presented for a generic conservation law and its property-preserving capability is proved on linear advection tests, in which it proves the preservation of strong gradients and the ability of controlling overshoots-undershoots. Even though the TVD property is not guaranteed, the numerical oscillations are greatly reduced. Then, the method is adapted to solve the convection-diffusion transport scalar equation with source terms, which is the core of any reacting flow simulation. The implementation is validated with the one-dimensional flame problem and then is tested in a turbulent combustion case. The comparison between the results obtained with conventional methods based on high-dissipation and the proposed low-dissipative approach shows clear benefits of the later, the interfaces are sharper and there is an improvement in the representation of the flame front. This formulation also shows capability to capture much more flow structures which make the simulation a closer representation of the actual physics.