Nektar++

简介

Nektar++ is a spectral/hp element framework designed to support the construction of efficient high-performance scalable solvers for a wide range of partial differential equations.

Nektar++使用说明

1. 求解二维方形区域的对流方程(pi2.0上单核串行)

image1

其中，\(x_b 和 y_b 代表计算域边界，V_x=2，V_y=3，\kappa=2\pi\)。

  1. 从 Nektar 官网 的GETTING STARTED->Tutorials->Basics->Advection-Diffusion->Introduction->Goals板块下载所需要的数据文件basics-advection-diffusion.tar.gz并解压；

  2. 解压之后会得到两个目录completed以及tutorial；

  3. 进入completed目录会看到如下几个文件：

ADR_conditions.xml

ADR_mesh.geo

ADR_mesh.msh

ADR_mesh.xml

ADR_mesh_aligned.fld

ADR_mesh_aligned.xml

这几个文件定义了求解本问题所需要的几何信息、网格信息以及初始和边界条件。

  1. 在此目录下编写如下Nektar_run.slurm脚本：

#!/bin/bash

#SBATCH -J Nektar_test
#SBATCH -p small
#SBATCH -n 1
#SBATCH --ntasks-per-node=1
#SBATCH -o %j.out
#SBATCH -e %j.err

module load nektar/5.0.0-intel-19.0.4-impi

ulimit -s unlimited
ulimit -l unlimited

ADRSolver ADR_mesh_aligned.xml ADR_conditions.xml

  1. 使用如下指令提交：

sbatch Nektar_run.slurm

  1. 然后即可在.out文件中看到如下结果：

=========================================
              EquationType: UnsteadyAdvection
              Session Name: ADR_mesh_aligned
              Spatial Dim.: 2
        Max SEM Exp. Order: 5
            Expansion Dim.: 2
            Riemann Solver: Upwind
            Advection Type:
           Projection Type: Discontinuous Galerkin
                 Advection: explicit
                 Diffusion: explicit
                 Time Step: 0.001
              No. of Steps: 1000
       Checkpoints (steps): 100
          Integration Type: ClassicalRungeKutta4
==========================================
Initial Conditions:
- Field u: sin(k*x)*cos(k*y)
Writing: "ADR_mesh_aligned_0.chk"
Steps: 100      Time: 0.1          CPU Time: 0.435392s
Writing: "ADR_mesh_aligned_1.chk"
Steps: 200      Time: 0.2          CPU Time: 0.430588s
Writing: "ADR_mesh_aligned_2.chk"
Steps: 300      Time: 0.3          CPU Time: 0.428503s
Writing: "ADR_mesh_aligned_3.chk"
Steps: 400      Time: 0.4          CPU Time: 0.428529s
Writing: "ADR_mesh_aligned_4.chk"
Steps: 500      Time: 0.5          CPU Time: 0.430142s
Writing: "ADR_mesh_aligned_5.chk"
Steps: 600      Time: 0.6          CPU Time: 0.429481s
Writing: "ADR_mesh_aligned_6.chk"
Steps: 700      Time: 0.7          CPU Time: 0.433232s
Writing: "ADR_mesh_aligned_7.chk"
Steps: 800      Time: 0.8          CPU Time: 0.431088s
Writing: "ADR_mesh_aligned_8.chk"
Steps: 900      Time: 0.9          CPU Time: 0.427919s
Writing: "ADR_mesh_aligned_9.chk"
Steps: 1000     Time: 1            CPU Time: 0.436098s
Writing: "ADR_mesh_aligned_10.chk"
Time-integration  : 4.31097s
Writing: "ADR_mesh_aligned.fld"
-------------------------------------------
Total Computation Time = 4s
-------------------------------------------
L 2 error (variable u) : 0.00863475
L inf error (variable u) : 0.0390366

2. 可压缩圆柱绕流(pi2.0上多核并行)

  1. 从 Nektar 官网 的GETTING STARTED->Tutorials->Compressible Flow Solver->Subsonic Cylinder->Introduction->Goals板块下载所需要的数据文件cfs-CylinderSubsonic_NS.tar.gz并解压；

  2. 解压之后会得到两个目录completed以及tutorial；

  3. 在tutorial目录下编写以下Nektar_run.slurm脚本：

#!/bin/bash

#SBATCH -J Nektar_test
#SBATCH -p cpu
#SBATCH -N 1
#SBATCH --ntasks-per-node=40
#SBATCH --exclusive
#SBATCH -o %j.out
#SBATCH -e %j.err

module load nektar/5.0.0-intel-19.0.4-impi
module load openmpi/3.1.5-gcc-9.2.0

ulimit -s unlimited
ulimit -l unlimited

mpirun -np 32 CompressibleFlowSolver CylinderSubsonic_NS.xml

  1. 使用如下指令提交：

sbatch Nektar_run.slurm

  1. 作业运行完毕后即可在.out文件中看到如下结果(部分)：

=======================================================================
              EquationType: NavierStokesCFE
              Session Name: CylinderSubsonic_NS
              Spatial Dim.: 2
        Max SEM Exp. Order: 3
            Expansion Dim.: 2
            Riemann Solver: HLLC
            Advection Type:
           Projection Type: Discontinuous Galerkin
            Diffusion Type:
                 Advection: explicit
             AdvectionType: WeakDG
                 Diffusion: explicit
                 Time Step: 1e-05
              No. of Steps: 60000
       Checkpoints (steps): 400
          Integration Type: RungeKutta
=======================================================================
=======================================================================
              EquationType: NavierStokesCFE
              Session Name: CylinderSubsonic_NS
              Spatial Dim.: 2
        Max SEM Exp. Order: 3
            Expansion Dim.: 2
            Riemann Solver: HLLC
            Advection Type:
           Projection Type: Discontinuous Galerkin
            Diffusion Type:
=======================================================================

3. 在思源一号上通过镜像来使用Nektar++

  1. 参考上文内容(求解对流方程)从 Nektar 官网 下载所需要的数据文件并解压，然后进入对应目录，在该目录下编写以下Nektar_run.slurm脚本：

#!/bin/bash

#SBATCH --job-name=nektar
#SBATCH --partition=64c512g
#SBATCH -N 1
#SBATCH --ntasks-per-node=2
#SBATCH --exclusive
#SBATCH --output=%j.out
#SBATCH --error=%j.err

module load openmpi/4.1.1-gcc-8.5.0

IMAGE_PATH=/dssg/share/imgs/nektar++/nek.sif
mpirun -np 2 singularity exec $IMAGE_PATH ADRSolver ADR_mesh_aligned.xml ADR_conditions.xml

  1. 使用如下指令提交：

sbatch Nektar_run.slurm

  1. 作业运行完毕之后即可在.out文件当中看到如下结果：

 gs_setup: 30 unique labels shared
 pairwise times (avg, min, max): 2.58603e-06 2.51303e-06 2.65902e-06
 crystal router                : 2.64363e-06 2.61022e-06 2.67704e-06
 all reduce                    : 2.46682e-06 2.36742e-06 2.56621e-06
 used all_to_all method: allreduce
 handle bytes (avg, min, max): 1588 1588 1588
 buffer bytes (avg, min, max): 480 480 480
 =======================================================================
              EquationType: UnsteadyAdvection
              Session Name: ADR_mesh_aligned
              Spatial Dim.: 2
        Max SEM Exp. Order: 5
            Num. Processes: 2
            Expansion Dim.: 2
            Riemann Solver: Upwind
            Advection Type: Weak DG
           Projection Type: Discontinuous Galerkin
       Advect. advancement: explicit
       Advect. advancement: explicit
                 Time Step: 0.001
              No. of Steps: 1000
       Checkpoints (steps): 100
          Integration Type: RungeKutta
=======================================================================
Initial Conditions:
- Field u: sin(k*x)*cos(k*y)
Writing: "ADR_mesh_aligned_0.chk" (0.000970838s, XML)
Steps: 100      Time: 0.1          CPU Time: 0.0535671s
Writing: "ADR_mesh_aligned_1.chk" (0.000835073s, XML)
Steps: 200      Time: 0.2          CPU Time: 0.0540179s
Writing: "ADR_mesh_aligned_2.chk" (0.000772003s, XML)
Steps: 300      Time: 0.3          CPU Time: 0.0542538s
Writing: "ADR_mesh_aligned_3.chk" (0.000588066s, XML)
Steps: 400      Time: 0.4          CPU Time: 0.0534871s
Writing: "ADR_mesh_aligned_4.chk" (0.000543744s, XML)
Steps: 500      Time: 0.5          CPU Time: 0.0529716s
Writing: "ADR_mesh_aligned_5.chk" (0.000545313s, XML)
Steps: 600      Time: 0.6          CPU Time: 0.0532116s
Writing: "ADR_mesh_aligned_6.chk" (0.000557265s, XML)
Steps: 700      Time: 0.7          CPU Time: 0.0532916s
Writing: "ADR_mesh_aligned_7.chk" (0.000709478s, XML)
Steps: 800      Time: 0.8          CPU Time: 0.0533924s
Writing: "ADR_mesh_aligned_8.chk" (0.000791041s, XML)
Steps: 900      Time: 0.9          CPU Time: 0.0534512s
Writing: "ADR_mesh_aligned_9.chk" (0.000566883s, XML)
Steps: 1000     Time: 1            CPU Time: 0.0532088s
Writing: "ADR_mesh_aligned_10.chk" (0.000583935s, XML)
Time-integration  : 0.534853s
renaming "ADR_mesh_aligned.fld" -> "ADR_mesh_aligned.bak0.fld"
Writing: "ADR_mesh_aligned.fld" (0.0112913s, XML)
-------------------------------------------
Total Computation Time = 1s
-------------------------------------------
L 2 error (variable u) : 0.00863475
L inf error (variable u) : 0.0390366

在自己的目录下自行安装Nektar++

  1. 执行以下从命令从GitHub上下载Nektar++源码：

git clone http://gitlab.nektar.info/nektar/nektar.git nektar++

  1. 下载完成后进入nektar++目录并通过源码编译安装(编译之前需要配置很多可选的编译选项，用户根据自己的具体情况自行选择即可)：

cd nektar++
mkdir build && cd build
ccmake ../
make
make install

参考资料

最后更新: 2024 年 11 月 22 日