论文标题
耦合Navier-Stokes和Gross-Pitaevskii方程，用于两流体量子流的数值模拟
Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows
论文作者
论文摘要
已建立了用于求解经典（或正常）粘性流体的Navier-Stokes方程的数值方法。总pitaevskii方程也是这种情况，在零温度限制中管理量子无关流动（或超氟）。在量子流中，例如在零至2.17 K之间的中等温度下的液体氦II，一种正常的流体和具有独立速度场的超流体共存。此类系统的最先进的现有模型使用Navier-Stokes方程进行普通流体，并根据量化重新连接规则的量化涡流丝的动力学来简化超流体的描述。在全球模型中，一次尝试将Navier-Stokes和Gross-Pitaevskii方程与纳入Navier-Stokes和Gross-Pitaevskii方程进行一次尝试（C. Coste，欧洲物理期刊B-浓缩物质和复杂系统）。我们在这一贡献中提出了一种新的数值模型，将不可压缩的流体与毛毛皮式液体融为一体。 Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii based on a slip velocity respecting the dynamics of vortex lines in the normal fluid.提出了一种基于伪 - 光谱傅里叶方法的数值算法，用于求解方程耦合系统。从字面上看，我们在数值上测试并验证了针对众所周知的基准测试新的数值系统，以在不同类型的正常流体中，用于不同类型的量化量子或量化量级的量化量级的基准（Vortex Crystal，Vortex，Vortex，Vortex Dipole and vortex dipole and vortex rings）。新的耦合模型为重新访问和丰富了复杂量子流体的现有数值结果开辟了新的可能性。
Numerical methods for solving the Navier-Stokes equations for classical (or normal) viscous fluids are well established. This is also the case for the Gross-Pitaevskii equation, governing quantum inviscid flows (or superfluids) in the zero temperature limit. In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt (C. Coste, The European Physical Journal B - Condensed Matter and Complex Systems, 1998) to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II. We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid. Coupling terms in the global system of equations involve new definitions of the following concepts: the regularized superfluid vorticity and velocity fields, the friction force exerted by quantized vortices to the normal fluid, the covariant gradient operator in the Gross-Pitaevskii based on a slip velocity respecting the dynamics of vortex lines in the normal fluid. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations.Finally, we numerically test and validate the new numerical system against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings). The new coupling model opens new possibilities to revisit and enrich existing numerical results for complex quantum fluids.
