Abstract
The Tadmor-type entropy conservative method using the mathematical logarithmic entropy function and two forms of the Sjogreen & Yee entropy conservative methods using the Harten entropy function are examined for their nonlinear stability and accuracy in very long time integration of the Euler equations of compressible gas dynamics. Following the same procedure as Ranocha [6] these entropy conservative methods can be made kinetic energy preserving with minimum added computational effort. The focus of this work is to examine the nonlinear stability and accuracy of these newly introduced high order entropy conserving and kinetic energy preserving methods for very long time integration of selected test cases when compared with their original methods. Computed entropy, and kinetic energy errors for these methods are compared with the Ducros et al. and the Kennedy-Gruber-Pirozzoli skew-symmetric splittings.
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