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

Abstract

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. Program summaryProgram Title: SemtexProgram Files doi:http://dx.doi.org/10.17632/65mz2szz5t.1Code Ocean Capsule:https://doi.org/10.24433/CO.2589809.v1Licensing provisions: GPLv2Programming languages: C++, C, Fortran77External routines: BLAS, LAPACK, yacc/bison, (optionally) MPINature of problem: Two- or three-dimensional incompressible Navier–Stokes in cylindrical and periodic Cartesian geometries with optional body forces. Two- or three-component velocity fields.Solution method: Continuous Galerkin nodal spectral element–Fourier spatial discretisation with semi-implicit time-splitting-based temporal integration of the nonlinear, viscous and pressure gradient terms in the Navier–Stokes equations via a projection method.