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Mitigating the impact of waves leaving a numerical domain has been apersistent challenge in numerical modeling. Reducing wave reflection at thedomain boundary is crucial for accurate simulations. Absorbing layers, whilecommon, often incur significant computational costs. This paper introduces anefficient application of a Legendre-Laguerre basis for absorbing layers fortwo-dimensional non-linear compressible Euler equations. The method couples aspectral-element bounded domain with a semi-infinite region, employing a tensorproduct of Lagrange and scaled Laguerre basis functions. The semi-infiniteregion serves as an absorbing layer for our simulations. In comparison toexisting methods with similar absorbing layer extensions, our approach, apioneering application to the Euler equations, demonstrates substantialcomputational savings. The study marks the first application of semi-infiniteelements to mitigate wave reflection in the solution of the Euler equations,particularly in nonhydrostatic atmospheric modeling. A comprehensive set oftests demonstrates the method's versatility for general systems of conservationlaws, with a focus on its effectiveness in damping vertically propagatinggravity waves in a linear hydrostatic mountain simulation a benchmark foratmospheric models. Across all tests, our model consistently exhibits notableperformance improvements compared to a traditional Rayleigh damping approach.

Efficient Spectral Element Method for the Euler Equations on Unbounded Domains in Multiple Dimensions