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后台阶流2023-07-17

算例说明

        后台阶流是一个经典的激波绕射数值模拟验证算例,5.09马赫的激波通过后台阶后存在很强的密度梯度,可以很好验证求解器的鲁棒性和求解精度。计算域长14m,高11m,进口边界存在高6m、宽1m的台阶。

几何.PNG

图1: 几何尺寸


工况条件

        工质无粘理想气体,初始时刻在x=0.5m,6m≤y≤11m处存在5.09马赫的激波,向右运动至密度ρ = 1.4kg/m3, 压强p = 1Pa的流场,激波速度通过朗金雨贡纽关系式得出。


计算网格

        xy平面划分为均匀网格,单元网格长度50mm,z方向一层网格,总计网格量5.9万。

网格.png

图2:网格

求解配置

  • 采用Dimaxer四代求解器进行5阶精度求解,5阶精度每个六面体单元对应125个自由度,5.92万网格对应740万自由度

  • 计算总时间为2.3s,可与参考文献结果进行对比

  • 部分配置json文件如下

"control": {
        "case_name": "back-step",
        "n_bundles": 8,
        "max_side_group_size": 2000,
        "solver_signature": "ns-ideal-cr-k4",
        "start_time": 0.0,
        "end_time": 2.3,
        "monitor_time_interval": 0.0023,
        "solution_output_time_interval": 0.023,
        "hardware_device_id": 6
    },
    "mesh_info": {
        "mesh_file_name": "geomAndMesh/backstep.dmh"
    },
    "boundary_info": {
        "far_field_conditions": [
            {
                "bc_name": "inlet",
                "bc_id_list": [
                    6
                ],
                "alpha": [
                    1.0,
                    0.0,
                    0.0
                ],
                "mach_inf": 1.6680471036740914,
                "pres_inf": 30.05945,
                "temp_inf": 4.269121233389778
            },
            {
                "bc_name": "outlet",
                "bc_id_list": [
                    10
                ],
                "alpha": [
                    1.0,
                    0.0,
                    0.0
                ],
                "mach_inf": 0.0,
                "pres_inf": 1.0,
                "temp_inf": 0.7142857142857143
            }
        ],
        "wall_conditions": [],
        "symmetry_conditions": [
            {
                "bc_name": "sym",
                "bc_id_list": [
                    5,
                    7,
                    8,
                    9
                ],
                "velocity": [
                    0.0,
                    0.0,
                    0.0
                ]
            }
        ]
    }

结果分析与计算时间统计

结果.gif图4: 动态结果


表1 计算时间统计

Run_ID
网格量阶次自由度说明GPU个数计算用时
run0159200五阶7400000z方向单层网格135.6min


参考文献

Jie Du, etc. A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework on unstructured meshes. Applied Numerical Mathematics 90 (2015) 146–167.







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