Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes

It is shown that the set of computable local symmetries of the G-equation for flame front propagation of premixed combustion is considerably extended if higher-order symmetries are considered. Classical point symmetries are exhaustively discussed in [13]. Further, if the flow velocity is zero, an infinite series of higher-order symmetries has been derived in [14]. Presently we show that the G-equation also admits an infinite number of higher-order symmetries for an arbitrary velocity field. Higher-order symmetries involving derivatives up to second order are computed. Geometrical and kinematic interpretations of the symmetries are given. For the special case of constant flow velocity, an infinite set of local conservation laws of the G-equation has been derived using the direct method. It is demonstrated how the derived infinite sets of local symmetries and conservation laws can be used to develop novel numerical schemes (including higherorder ones) to perform computations in practical applications involving the G-equation.