论文标题
抑制热力学截短的无粘性方程中的热化和构建弱解决方案：汉堡方程的教训
Suppressing thermalization and constructing weak solutions in truncated inviscid equations of hydrodynamics: Lessons from the Burgers equation
论文作者
论文摘要
有限维度的流体动力学方程，例如零粘度，一维汉堡方程或三维不可压缩的Euler方程，通过傅立叶 - 盖尔金投影获得，通过一种结构介导的结构，通过称为tygers的结构介导[ray等。 Rev. E 84，016301（2011）] ---带有能量等级。因此，通常必须将galerkin截断的无粘性部分微分方程的数值解显示出与母体方程不一致的行为。现在，我们通过使用一维汉堡方程作为测试地面提出一种新型的数值配方，称为Tyger净化，以阻止热量的发作，从而恢复了真正的耗散溶液。
Finite-dimensional, inviscid equations of hydrodynamics, such as the zero-viscosity, one-dimensional Burgers equation or the three-dimensional incompressible Euler equation, obtained through a Fourier-Galerkin projection, thermalise---mediated through structures known as tygers [Ray et al., Phys. Rev. E 84, 016301 (2011)]---with an energy equipartition. Therefore, numerical solutions of inviscid partial differential equations, which typically have to be Galerkin-truncated, show a behaviour at odds with the parent equation. We now propose, by using the one-dimensional Burgers equation as a testing ground, a novel numerical recipe, named tyger purging, to arrest the onset of thermalisation and hence recover the true dissipative solution.
