We show that a specific skew-symmetric form of hyperbolic problems leads to energy conservation and an energy bound. Next, the compressible Euler equations is transformed to this skew-symmetric form and it is explained how to obtain an energy estimate. Finally we show that the new formulation lead to energy stable and energy conserving discrete approximations if the scheme is formulated on summation-by-parts form.
翻译:我们显示,一种特定的双曲问题对称形式导致节能和能源结合。 其次,可压缩的欧拉方程式转换成这种对称形式,并解释如何获得能源估计。 最后,我们表明,如果计划是按逐部分制成的,新配方可导致能源稳定和节能离散近似值。