论文标题
不可压缩的欧拉流动中异常能量耗散的数值证据：迈向无粘性泰勒绿色问题的网格结合结果
Numerical evidence of anomalous energy dissipation in incompressible Euler flows: Towards grid-converged results for the inviscid Taylor-Green problem
论文作者
论文摘要
在三个空间维度下提供不可压缩的欧拉方程有限的奇异性的证据仍然是一个未解决的问题。同样，迄今为止，数值实验尚未证明湍流的零核法。我们通过使用一种新型的高阶不连续的Galerkin离散化方法对Inviscid的三维泰勒绿色涡流问题进行高分辨率数值模拟解决这个问题。我们的主要发现是，动能演化并不倾向于为增加数值方案的空间分辨率而倾向于精确的能量保存，而是会收敛到具有非零动能耗能耗散速率的溶液。这意味着根据Onsager的猜想，能量耗散异常在粘性耗散的情况下，这是不可压缩的Inviscid流中有限的奇异性的指示。我们证明了三维无关的泰勒绿色问题的汇聚解决方案，对于动能的时间演变，计量的相对$ l_2 $ error $ 0.27 \％$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $。
Providing evidence of finite-time singularities of the incompressible Euler equations in three space dimensions is still an unsolved problem. Likewise, the zeroth law of turbulence has not been proven to date by numerical experiments. We address this issue by high-resolution numerical simulations of the inviscid three-dimensional Taylor-Green vortex problem using a novel high-order discontinuous Galerkin discretization approach. Our main finding is that the kinetic energy evolution does not tend towards exact energy conservation for increasing spatial resolution of the numerical scheme, but instead converges to a solution with nonzero kinetic energy dissipation rate. This implies an energy dissipation anomaly in the absense of viscous dissipation according to Onsager's conjecture, and serves as an indication of finite-time singularities in incompressible inviscid flows. We demonstrate convergence to a dissipative solution for the three-dimensional inviscid Taylor-Green problem with a measured relative $L_2$-error of $0.27 \%$ for the temporal evolution of the kinetic energy and $3.52 \%$ for the kinetic energy dissipation rate.
