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Abstract |
G-equations are level set Hamilton-Jacobi equations (HJE) for modeling flame fronts in turbulent combustion where a fundamental problem is to characterize the turbulent flame speeds s_T. We show that the existence of s_T is connected with the homogenization of HJE, however classical theory does not apply and new mathematics must be developed to address the non-coercive and non-convex nature ofthe level set Hamiltonian. We shall illustrate the asymptotic properties of s_T from both Eulerian and Lagrangian perspectives in the case of two dimensional periodic incompressible flows, in particular cellular flows. Analytical and numerical results demonstrate that G-equations capture well the enhancement, slow down and quenching phenomena observed in experiments. This is joint work with Yifeng Yu and Yu-Yu Liu. |
