ABSTRACT
The full compressible Euler equations in gas dynamics have the form () https://www.w3.org/1998/Math/MathML"> { ρ t + ∇ · ( ρ U ) = 0 , ( ρ U ) t + ∇ · ( ρ U ⊗ U ) + ∇ p = 0 , ( ρ E ) t + ∇ · ( ρ U ( E + p ρ ) ) = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203719138/327a1a91-9d2a-45fb-882a-fc814ebe8457/content/eq2451.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where https://www.w3.org/1998/Math/MathML"> E = | U | 2 2 + e https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203719138/327a1a91-9d2a-45fb-882a-fc814ebe8457/content/eq2452.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is the total energy, ρ(t, X) (X = (x, y)) the density, U = (u, v) the velocity, and e is the internal energy. For a polytropic gas https://www.w3.org/1998/Math/MathML"> e = p ( γ − 1 ) ρ , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203719138/327a1a91-9d2a-45fb-882a-fc814ebe8457/content/eq2453.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where γ > 1 is a constant, and γ = 1.4 for air. Our forthcoming numerical results are obtained for this index.
