On the construction of PML absorbing boundary condition for the non-linear Euler equations

A Perfectly Matched Layer (PML) absorbing boundary condition for the nonlinear Euler equations in two space dimensions is presented. The derivation of PML equation follows athree-step method recently developed for the PML of linearized Euler equations. Two versions of time-domain PML equations are given. One uses unsplit physical variables and the other uses the split equation in the derivation but requires fewer auxiliary variables. Both versions are given for the nonlinear Euler equation written in the conservation form, so they can be implemented easily in most existing codes. To increase the efficiency of the PML, a pseudo mean-flow is introduced in the derivation of the PML equations. The proposed PML absorbs exponentially the difference between the nonlinear total variable and a prescribed pseudo mean flow. Moreover, the non-linear PML reduces to the linearized PML upon linearization about the pseudo mean-flow. The validity and efficiency of PML as an absorbing boundary condition for non-linear Euler equations are demonstrated by numerical examples, including the absorption of an isentropic vortex, a nonlinear pressure pulse and roll-up vortices of shear flows. Satisfactory computational results are reported.

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