Semtex: A spectral element–Fourier solver for the incompressible Navier–Stokes equations in cylindrical or Cartesian coordinates

Semtex enables direct numerical simulation (DNS) of the incompressible Navier–Stokes equations by coupling continuous-Galerkin nodal spectral element–Fourier spatial discretisation with semi-implicit temporal integration via a time-splitting scheme. Transport of a scalar quantity may be included. The analyst has a choice of Cartesian or cylindrical coordinate systems. Domain geometries and solutions may be two-dimensional with spectral element decomposition of arbitrary planar shapes, or made three-dimensional by extrusion along a spatially homogeneous direction in which Fourier expansions are employed. For three-dimensional solutions, MPI may be used to support parallel execution. Various body forces, including Boussinesq buoyancy and Coriolis terms may be added to the momentum equation to simulate e.g. the effects of stratification and thermal expansion or reference frame rotation. Parallel decomposition is performed in the Fourier dimension only, and two-dimensional elliptic systems in the plane are solved for the spectral element discretisation using direct (Cholesky) or iterative (conjugate-gradient) methods. Semtex includes a suite of additional tools for generating initial conditions and model configurations, for post processing and for analysis of model output.

Semtex可通过将连续伽辽金节点谱元-傅里叶空间离散方法与基于时间分裂格式的半隐式时间积分方案相结合，实现不可压缩纳维-斯托克斯（Navier–Stokes）方程的直接数值模拟（direct numerical simulation, DNS）。该工具支持标量物理量的输运模拟，使用者可选用笛卡尔坐标系或圆柱坐标系作为计算坐标系。计算域几何与求解结果可采用二维模式：可对任意平面形状进行谱元分解；也可通过沿空间均匀方向拉伸拓展至三维构型，该方向上采用傅里叶展开进行离散。针对三维求解场景，可采用消息传递接口（Message Passing Interface, MPI）以支持并行执行。动量方程中可添加多种体力项，包括布辛涅斯克（Boussinesq）浮力项与科里奥利（Coriolis）项，以模拟层化、热膨胀或参考系旋转等物理效应。并行分解仅在傅里叶维度上进行，针对谱元离散的平面二维椭圆系统，可采用直接（乔列斯基（Cholesky）分解）或迭代（共轭梯度（conjugate-gradient）法）方法进行求解。Semtex还集成了一套完整的辅助工具集，可用于生成初始条件与模型配置、后处理以及模型输出结果的分析。