Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5):1940-1967, 2002) and for the Euler equations of compressible fluid flow in Sjogreen and Peterson (Commun. Comput. Phys. 2:1199-1219, 2007), to the compressible Navier-Stokes equations.  describe the method and  implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
['Marco Kupiainen', 'Björn Sjögreen']
I am writing a research paper on a idea A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
[{"from": "human", "value": "I am writing a research paper on a idea A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5):1940-1967, 2002) and for the Euler equations of compressible fluid flow in Sjogreen and Peterson (Commun. Comput. Phys. 2:1199-1219, 2007), to the compressible Navier-Stokes equations.  describe the method and  implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization."}]