Abstract Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems. VMS methods avoid the assumption of separable nonlinearity and the reliance on empirical small-scale models by using a variational decomposition of scales together with a residual-based approximation of the small-scales. Evaluation of a nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems arising from fluid flow models. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn treats the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. The VMSn approach is complemented with two algebraic approximations of the small-scales: one based on the main diagonal of the transport matrices and another that preserves transport fluxes and is suitable for generic TADR systems. The suitability of the VMSn approach for handling general TADR problems and regimes is evaluated with benchmark incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, the turbulent free jet, and the two-temperature arc in crossflow. Simulation results show that VMSn leads to minor improvements in accuracy with respect to the classical VMS for the laminar flow problems, but to significantly greater accuracy for the turbulent flows and the unsteady plasma flow problems, while using the same cohesive numerical formulation.

中文翻译：

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流体输送问题的非线性变分多尺度方法的评估

摘要 各种传输问题，尤其是基于流体流动模型的传输问题，本质上是多尺度和非线性的，这些特征通常会导致复杂的动力学，例如不稳定性和湍流的发展。解决这些问题中所有尺度的计算模拟通常是不可行的，这促使采用粗粒度模拟策略，其中对小尺度特征进行建模而不是解决。变分多尺度 (VMS) 方法，特别是基于残差的大涡模拟 (LES) 方法，已被证明对于复杂传输问题的粗粒度模拟是有效且稳健的。VMS 方法通过使用尺度的变分分解以及基于残差的小尺度近似，避免了可分离非线性的假设和对经验小尺度模型的依赖。非线性 VMS 方法的评估，表示为 VMSn，用于粗粒度模拟由流体流动模型引起的瞬态平流扩散反应 (TADR) 传输问题。与忽略小尺度对运输运营商影响的经典 VMS 方法相比，VMSn 预先处理了大尺度和小尺度之间的相互依赖性。尺度间耦合的处理涉及描述小尺度演化的局部代数非线性系统的解决方案。VMSn 方法补充了两个小尺度的代数近似：一种基于传输矩阵的主对角线，另一种保留传输通量并适用于通用 TADR 系统。VMSn 方法处理一般 TADR 问题和状态的适用性通过基准不可压缩、可压缩和磁流体动力学层流问题、不可压缩泰勒-格林涡流、湍流自由射流和交叉流中的双温度弧进行评估。仿真结果表明，相对于经典 VMS，VMSn 在层流问题上的精度略有提高，但在湍流和非定常等离子体流问题上的精度显着提高，同时使用相同的内聚数值公式。