论文标题
可压缩流的新的耗散控制，多尺度解决方案的新范式
A new paradigm of dissipation-controllable, multi-scale resolving schemes for compressible flows
论文作者
论文摘要
通过直接数值模拟（DNS）或大型涡流模拟（LES）对高速压缩流的尺度解析模拟需要冲击捕捉方案更准确，以解决宽带湍流，并强大地捕获强烈的冲击波。在这项工作中，我们开发了一种新的可耗散，可冲击捕获方案的范式，以解决高速压缩流中的多尺度流量结构。这种新颖的冲击捕获方案范式被称为PNTM-BVD-CD。提出的PNTM-BVD-CD方案具有以下理想的特性。首先，它可以捕获大规模的不连续结构，例如强烈的冲击波，而无需明显的非物理振荡，同时解决尖锐的接触，材料界面和剪切层。其次，可以通过简单的可调参数$λ$在n+1阶向上偏向偏置方案和非脉冲n+2阶中心方案之间有效控制PNTM-BVD-CD的数值耗散属性。第三，在$λ= 0.5 $的情况下，该方案可以恢复到n+2阶的非隔离中心插值，以在所有波数上平滑溶液，这是在DNS中求解小规模结构以及在显式LES中可分解的规模的优选。最后，通过所谓的隐式LE（ILES）方法，可以通过耗散可控算法来求解溶解不足的小尺度。
The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-controllable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. This novel paradigm of shock-capturing scheme is named as PnTm-BVD-CD. The proposed PnTm-BVD-CD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of PnTm-BVD-CD can be effectively controlled between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter $λ$. Thirdly, with $λ=0.5$ the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with dissipation controllable algorithm through so-called implicit LES (ILES) approach.
