forked from p35462178/gks2d-str
525 lines
18 KiB
C++
525 lines
18 KiB
C++
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#include"accuracy_test.h"
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void accuracy_sinwave_1d()
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{
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int mesh_set = 3; //用一系列网格尺寸等比例减小的网格来测试格式的精度
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int mesh_number_start = 10; //最粗网格数
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double length = 2.0; //计算域总长度为2，[0,2]
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double CFL = 0.5; //CFL数
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// 注意，为了防止时间推进和空间离散的精度不一致，dt = CFL * （dx^dt_ratio），这一点的原因也可以参看
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// X. Ji et al. Journal of Computational Physics 356 (2018) 150–173 的 subsection 4.1
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double dt_ratio = 1.0;
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//end
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double mesh_size_start = length / mesh_number_start; //均匀网格大小
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//各套网格数量-尺寸-误差 开辟数组存一下
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int* mesh_number = new int[mesh_set];
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double* mesh_size = new double[mesh_set];
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double** error = new double* [mesh_set];
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//end
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for (int i = 0; i < mesh_set; i++)
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{
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error[i] = new double[3]; //每一套网格都计算 L1 L2 L_inf 误差
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mesh_size[i] = mesh_size_start / pow(2, i); //等比变化
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mesh_number[i] = mesh_number_start * pow(2, i); //等比变化
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//计算每一套网格的工况,得到对应的误差
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accuracy_sinwave_1d(CFL, dt_ratio, mesh_number[i], error[i]);
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//end
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}
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output_error_form(CFL, dt_ratio, mesh_set, mesh_number, error);
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}
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void accuracy_sinwave_1d(double& CFL, double& dt_ratio, int& mesh_number, double* error)
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{
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Runtime runtime;//记录一下计算时间
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runtime.start_initial = clock();
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Block1d block; //存储一些一维算例相关的基本信息
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block.nodex = mesh_number;
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block.ghost = 3; // ghost cell 数。一般来讲 二阶-三阶 需要两个，四阶-五阶 需要三个。具体算法则需具体讨论
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double tstop = 2.0; //计算一个sinwave的周期
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block.CFL = CFL; // CFL数
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K = 4; //内部自由度
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Gamma = 1.4; //比热容是由内部自由度决定的，这里为了简单，直接手动给出
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tau_type = Euler; //无粘还是粘性问题
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//准备通量函数
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//函数指针 flux_function 可以方便的切换 使用的通量求解器
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//如 L-F， HLLC, GKS
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flux_function = GKS; //GKS
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//通常 GKS是指 2阶gks，但通过一些近似，可以变形为
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//一阶GKS（gks1st） 一阶KFVS(kfvs1st) 等，在gks1dsolver中枚举出来
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gks1dsolver = gks2nd; //现在选择二阶gks
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c1_euler = 0.0; //仅对于无粘流动，gks里面的人工碰撞时间系数c1
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c2_euler = 0.0; //对于无粘或者粘性流动，gks里面的人工碰撞时间系数c2
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//end
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//边界条件函数设定
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Fluid1d* bcvalue = new Fluid1d[2]; //一维左右dirichlet边界的值
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BoundaryCondition leftboundary(0);
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BoundaryCondition rightboundary(0);
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leftboundary = periodic_boundary_left;
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rightboundary = periodic_boundary_right;
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//end
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//设置重构函数
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cellreconstruction = WENO5_AO; //以单位为中心的重构，重构出界面左值和右值
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wenotype = wenoz; //非线性权的种类,linear就意味着采用线性权
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reconstruction_variable = characteristic; //重构变量的类型，分为特征量和守恒量
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g0reconstruction = Center_collision;//平衡态函数g0的重构方式（传统黎曼求解器用此函数得到粘性项所需要的一阶导数）
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//end
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//显式时间推进选取，支持N步M阶时间精度，N目前写死了小于等于5
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timecoe_list = S2O4;//这叫做2步4阶 two-stage fourth-order
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Initial_stages(block); //赋值一下
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//end
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// allocate memory for 1-D fluid field
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// in a standard finite element method, we have
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// first the cell average value, N
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block.nx = block.nodex + 2 * block.ghost;
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block.nodex_begin = block.ghost;
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block.nodex_end = block.nodex + block.ghost - 1;
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Fluid1d* fluids = new Fluid1d[block.nx];
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// then the interfaces reconstructioned value, N+1
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Interface1d* interfaces = new Interface1d[block.nx + 1];
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// then the flux, which the number is identical to interfaces
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Flux1d** fluxes = Setflux_array(block);
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//end the allocate memory part
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//bulid or read mesh,
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//since the mesh is all structured from left and right,
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//there is no need for buliding the complex topology between cells and interfaces
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//just using the index for address searching
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block.left = 0.0;
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block.right = 2.0;
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block.dx = (block.right - block.left) / block.nodex;
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//set the uniform geometry information
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SetUniformMesh(block, fluids, interfaces, fluxes);
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//初始化一下
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ICfor_sinwave(fluids, block);
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//初始化时间和时间步长
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block.t = 0;//the current simulation time
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block.step = 0; //the current step
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int inputstep = 1;//输入一个运行的时间步数
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runtime.finish_initial = clock(); //记录一下初始化需要的cpu时间....
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while (block.t < tstop) //显式时间步循环，from t^n to t^n+1
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{
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//输入一个运行时间步数的主要好处是，你可以在开发阶段，先让程序跑几步停一下看看结果
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//避免跑了一万步，发现从第一部就爆掉了
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if (block.step % inputstep == 0)
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{
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cout << "pls cin interation step, if input is 0, then the program will exit " << endl;
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cin >> inputstep;
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if (inputstep == 0)
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{
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output1d(fluids, block); //这个是输出一维的流场数据
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break;
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}
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}
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//记录运算时间
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if (runtime.start_compute == 0.0)
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{
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runtime.start_compute = clock();
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cout << "runtime-start " << endl;
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}
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//end
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//Copy the fluid vales to fluid old
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CopyFluid_new_to_old(fluids, block);
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//determine the cfl condtion
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block.dt = Get_CFL(block, fluids, tstop);
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for (int i = 0; i < block.stages; ++i)
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{
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//边界条件
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leftboundary(fluids, block, bcvalue[0]);
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rightboundary(fluids, block, bcvalue[1]);
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//重构
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Reconstruction_within_cell(interfaces, fluids, block);
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Reconstruction_forg0(interfaces, fluids, block);
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//计算通量
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Calculate_flux(fluxes, interfaces, block, i);
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//更新
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Update(fluids, fluxes, block, i);
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}
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block.step++;
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block.t = block.t + block.dt;
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if ((block.t - tstop) > 0)
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{
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error_for_sinwave(fluids, block, tstop, error);
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}
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}
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runtime.finish_compute = clock();
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cout << "initializiation time is " << (float)(runtime.finish_initial - runtime.start_initial) / CLOCKS_PER_SEC << "seconds" << endl;
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cout << "computational time is " << (float)(runtime.finish_compute - runtime.start_compute) / CLOCKS_PER_SEC << "seconds" << endl;
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output1d(fluids, block);
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}
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void ICfor_sinwave(Fluid1d* fluids, Block1d block)
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{
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#pragma omp parallel for
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for (int i = block.nodex_begin; i <= block.nodex_end; i++)
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{
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double pi = 3.14159265358979323846;
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fluids[i].primvar[0]
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= 1.0 - 0.2 / pi / block.dx *
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(cos(pi * (i + 1 - block.ghost) * block.dx) - cos(pi * (i - block.ghost) * block.dx));
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fluids[i].primvar[1] = 1;
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fluids[i].primvar[2] = 1;
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Primvar_to_convar_1D(fluids[i].convar, fluids[i].primvar);
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}
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}
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void error_for_sinwave(Fluid1d* fluids, Block1d block, double tstop, double* error)
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{
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if (abs(block.t - tstop) <= (1e-10))
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{
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double error1 = 0;
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double error2 = 0;
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double error3 = 0;
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for (int i = block.ghost; i < block.nx - block.ghost; i++)
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{
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double pi = 3.14159265358979323846;
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int index = i;
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double primvar0 = 1 - 0.2 / pi / block.dx * (cos(pi * (i + 1 - block.ghost) * block.dx) - cos(pi * (i - block.ghost) * block.dx));
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error1 = error1 + abs(fluids[index].convar[0] - primvar0);
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error2 = error2 + pow(fluids[index].convar[0] - primvar0, 2);
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error3 = (error3 > abs(fluids[index].convar[0] - primvar0)) ? error3 : abs(fluids[index].convar[0] - primvar0);
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}
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error1 /= block.nodex;
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error2 = sqrt(error2 / block.nodex);
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error[0] = error1; error[1] = error2; error[2] = error3;
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cout << scientific << "L1 error=" << error1 << " L2 error=" << error2 << " Linf error=" << error3 << endl;
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}
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}
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void accuracy_sinwave_2d()
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{
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int mesh_set = 3;
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int mesh_number_start = 10;
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double length = 2.0;
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double CFL = 0.5;
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double dt_ratio = 1.0;
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double mesh_size_start = length / mesh_number_start;
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int* mesh_number = new int[mesh_set];
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double* mesh_size = new double[mesh_set];
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double** error = new double* [mesh_set];
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for (int i = 0; i < mesh_set; ++i)
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{
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error[i] = new double[3];
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mesh_size[i] = mesh_size_start / pow(2, i);
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mesh_number[i] = mesh_number_start * pow(2, i);
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sinwave_2d(CFL, dt_ratio, mesh_number[i], error[i]);
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}
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output_error_form(CFL, dt_ratio, mesh_set, mesh_number, error);
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}
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void sinwave_2d(double& CFL, double& dt_ratio, int& mesh_number, double* error)
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{
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Runtime runtime;
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runtime.start_initial = clock();
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Block2d block; // Class, geometry variables
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block.uniform = false;
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block.nodex = mesh_number;
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block.nodey = mesh_number;
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block.ghost = 3; // 5th-order reconstruction, should 3 ghost cell
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double tstop = 2;
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block.CFL = CFL;
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K = 3; // 1d K=4, 2d K=3, 3d K=2;
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Gamma = 1.4; // diatomic gas, r=1.4
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//this part should rewritten ad gks2dsolver blabla
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gks2dsolver = gks2nd_2d; // Emumeration, choose solver type
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// 2nd means spatical 2nd-order, the traditional GKS; 2d means two dimensions
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tau_type = Euler; // Emumeration, choose collision time tau type
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// for accuracy test case, the tau type should be Euler and more accurately ZERO
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// for inviscid case, use Euler type tau; for viscous case, use NS type tau
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c1_euler = 0.0; // first coefficient in Euler type tau calculation
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c2_euler = 0.0; // second coefficient in Euler type tau calculation
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// when Euler type, tau is always zero;
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// if the c1 c2 were given, (c1, c2, should be given together), the tau_num is determined by c1 c2, (c1*dt + c2*deltaP)
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// if c1, c2 are both zero, (or not given value either), tau_num is also zero, which might be useful for accuracy test.
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// when NS type, tau is always physical tau, relating to Mu or Nu;
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// besides, tau_num would be determined by tau and c2 part, (tau + c2*deltaP),
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// so, c2 should be given (c1 is useless now), and Mu or Nu should be given ONLY ONE;
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// for NS type, specially, if Smooth is true, tau_num is determined ONLY by tau, (tau_num = tau), which means c2 is zero
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Mu = 0.0;
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Pr = 0.73;
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R_gas = 1;
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//prepare the boundary condtion function
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Fluid2d* bcvalue = new Fluid2d[4]; // Class, primitive variables only for boundary
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BoundaryCondition2dnew leftboundary(0); // 声明 边界条件的 函数指针
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BoundaryCondition2dnew rightboundary(0); // 声明 边界条件的 函数指针
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BoundaryCondition2dnew downboundary(0); // 声明 边界条件的 函数指针
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BoundaryCondition2dnew upboundary(0); // 声明 边界条件的 函数指针
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leftboundary = periodic_boundary_left; // 给函数指针 赋值
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rightboundary = periodic_boundary_right; // 给函数指针 赋值
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downboundary = periodic_boundary_down; // 给函数指针 赋值
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upboundary = periodic_boundary_up; // 给函数指针 赋值
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//prepare the reconstruction
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gausspoint = 2; // fifth-order or sixth-order use THREE gauss points
|
|||
|
|
// WENO5 has the function relating to arbitrary gausspoints
|
|||
|
|
// WENO5_AO supports 2 gausspoint now, so fourth-order at most for spacial reconstruction (enough for two step fourth-order GKS)
|
|||
|
|
SetGuassPoint(); // Function, set Gauss points coordinates and weight factor
|
|||
|
|
|
|||
|
|
reconstruction_variable = conservative; // Emumeration, choose the variables used for reconstruction type
|
|||
|
|
wenotype = linear; // Emumeration, choose reconstruction type
|
|||
|
|
|
|||
|
|
cellreconstruction_2D_normal = WENO5_normal; // reconstruction in normal directon
|
|||
|
|
cellreconstruction_2D_tangent = WENO5_tangent; // reconstruction in tangential directon
|
|||
|
|
g0reconstruction_2D_normal = Center_5th_normal; // reconstruction for g0 in normal directon
|
|||
|
|
g0reconstruction_2D_tangent = Center_5th_tangent; // reconstruction for g0 in tangential directon
|
|||
|
|
|
|||
|
|
|
|||
|
|
//prepare the flux function
|
|||
|
|
flux_function_2d = GKS2D_smooth; // 给函数指针 赋值 flux calculation type
|
|||
|
|
// solver is GKS
|
|||
|
|
// GKS2D means full solver (used for shock), GKS2D_smooth means smooth solver (used for non_shock)
|
|||
|
|
// for accuracy test case, tau is ZERO, so GKS2D is equal to GKS2D_smooth for results, but the later is faster
|
|||
|
|
// for inviscid flow, Euler type tau equals artifical viscosity;
|
|||
|
|
// for viscous flow, NS type tau equals the modified collision time;
|
|||
|
|
//end
|
|||
|
|
|
|||
|
|
//prepare time marching stratedgy
|
|||
|
|
//time coe list must be 2d, end by _2D
|
|||
|
|
timecoe_list_2d = S2O4_2D; // 两步四阶
|
|||
|
|
Initial_stages(block);
|
|||
|
|
|
|||
|
|
|
|||
|
|
// allocate memory for 2-D fluid field
|
|||
|
|
// in a standard finite element method, we have
|
|||
|
|
// first the cell average value, N*N
|
|||
|
|
block.nx = block.nodex + 2 * block.ghost;
|
|||
|
|
block.ny = block.nodey + 2 * block.ghost;
|
|||
|
|
|
|||
|
|
Fluid2d* fluids = Setfluid(block); // Function, input a class (geometry), output the pointer of one class (conservative variables)
|
|||
|
|
// then the interfaces reconstructioned value, (N+1)*(N+1)
|
|||
|
|
Interface2d* xinterfaces = Setinterface_array(block);
|
|||
|
|
Interface2d* yinterfaces = Setinterface_array(block);
|
|||
|
|
// then the flux, which the number is identical to interfaces
|
|||
|
|
Flux2d_gauss** xfluxes = Setflux_gauss_array(block);
|
|||
|
|
Flux2d_gauss** yfluxes = Setflux_gauss_array(block);
|
|||
|
|
//end the allocate memory part
|
|||
|
|
|
|||
|
|
block.left = 0.0;
|
|||
|
|
block.right = 2.0;
|
|||
|
|
block.down = 0.0;
|
|||
|
|
block.up = 2.0;
|
|||
|
|
block.dx = (block.right - block.left) / block.nodex;
|
|||
|
|
block.dy = (block.up - block.down) / block.nodey;
|
|||
|
|
block.overdx = 1 / block.dx;
|
|||
|
|
block.overdy = 1 / block.dy;
|
|||
|
|
//set the uniform geometry information
|
|||
|
|
SetUniformMesh(block, fluids, xinterfaces, yinterfaces, xfluxes, yfluxes); // Function, set mesh
|
|||
|
|
|
|||
|
|
//end
|
|||
|
|
|
|||
|
|
ICfor_sinwave_2d(fluids, block);
|
|||
|
|
|
|||
|
|
runtime.finish_initial = clock();
|
|||
|
|
block.t = 0; //the current simulation time
|
|||
|
|
block.step = 0; //the current step
|
|||
|
|
|
|||
|
|
int inputstep = 1;//input a certain step
|
|||
|
|
|
|||
|
|
while (block.t < tstop)
|
|||
|
|
{
|
|||
|
|
|
|||
|
|
if (block.step % inputstep == 0)
|
|||
|
|
{
|
|||
|
|
cout << "pls cin interation step, if input is 0, then the program will exit " << endl;
|
|||
|
|
cin >> inputstep;
|
|||
|
|
if (inputstep == 0)
|
|||
|
|
{
|
|||
|
|
output2d_binary(fluids, block); // 二进制输出，用单元中心点代替单元
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
if (runtime.start_compute == 0.0)
|
|||
|
|
{
|
|||
|
|
runtime.start_compute = clock();
|
|||
|
|
cout << "runtime-start " << endl;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
CopyFluid_new_to_old(fluids, block); // Function, copy variables
|
|||
|
|
//determine the cfl condtion
|
|||
|
|
block.dt = Get_CFL(block, fluids, tstop); // Function, get real CFL number
|
|||
|
|
|
|||
|
|
if ((block.t + block.dt - tstop) > 0)
|
|||
|
|
{
|
|||
|
|
block.dt = tstop - block.t + 1e-16;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
for (int i = 0; i < block.stages; i++)
|
|||
|
|
{
|
|||
|
|
//after determine the cfl condition, let's implement boundary condtion
|
|||
|
|
leftboundary(fluids, block, bcvalue[0]);
|
|||
|
|
rightboundary(fluids, block, bcvalue[1]);
|
|||
|
|
downboundary(fluids, block, bcvalue[2]);
|
|||
|
|
upboundary(fluids, block, bcvalue[3]);
|
|||
|
|
//cout << "after bc " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
|
|||
|
|
Convar_to_Primvar(fluids, block); // Function
|
|||
|
|
//then is reconstruction part, which we separate the left or right reconstrction
|
|||
|
|
//and the center reconstruction
|
|||
|
|
Reconstruction_within_cell(xinterfaces, yinterfaces, fluids, block); // Function
|
|||
|
|
//cout << "after cell recon " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
|
|||
|
|
Reconstruction_forg0(xinterfaces, yinterfaces, fluids, block); // Function
|
|||
|
|
//cout << "after g0 recon " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
|
|||
|
|
//then is solver part
|
|||
|
|
Calculate_flux(xfluxes, yfluxes, xinterfaces, yinterfaces, block, i); // Function
|
|||
|
|
//cout << "after flux calcu " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
|
|||
|
|
//then is update flux part
|
|||
|
|
Update(fluids, xfluxes, yfluxes, block, i); // Function
|
|||
|
|
//cout << "after updating " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
block.step++;
|
|||
|
|
block.t = block.t + block.dt;
|
|||
|
|
|
|||
|
|
if (block.step % 1000 == 0)
|
|||
|
|
{
|
|||
|
|
cout << "step 1000 time is " << (double)(clock() - runtime.start_compute) / CLOCKS_PER_SEC << endl;
|
|||
|
|
}
|
|||
|
|
if ((block.t - tstop) >= 0)
|
|||
|
|
{
|
|||
|
|
output2d_binary(fluids, block);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
error_for_sinwave_2d(fluids, block, tstop, error); // Function, get error
|
|||
|
|
runtime.finish_compute = clock();
|
|||
|
|
|
|||
|
|
cout << "the total run time is " << (double)(runtime.finish_compute - runtime.start_initial) / CLOCKS_PER_SEC << " second !" << endl;
|
|||
|
|
cout << "initializing time is" << (double)(runtime.finish_initial - runtime.start_initial) / CLOCKS_PER_SEC << " second !" << endl;
|
|||
|
|
cout << "the pure computational time is" << (double)(runtime.finish_compute - runtime.start_compute) / CLOCKS_PER_SEC << " second !" << endl;
|
|||
|
|
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void ICfor_sinwave_2d(Fluid2d* fluids, Block2d block)
|
|||
|
|
{
|
|||
|
|
for (int i = block.ghost; i < block.nx - block.ghost; i++)
|
|||
|
|
{
|
|||
|
|
for (int j = block.ghost; j < block.ny - block.ghost; j++)
|
|||
|
|
{
|
|||
|
|
double pi = 3.14159265358979323846;
|
|||
|
|
int index = i * (block.ny) + j;
|
|||
|
|
double xleft = (i - block.ghost) * block.dx;
|
|||
|
|
double xright = (i + 1 - block.ghost) * block.dx;
|
|||
|
|
double yleft = (j - block.ghost) * block.dy;
|
|||
|
|
double yright = (j + 1 - block.ghost) * block.dy;
|
|||
|
|
|
|||
|
|
//case in two dimensional x-y-plane
|
|||
|
|
double k1 = sin(pi * (xright + yright));
|
|||
|
|
double k2 = sin(pi * (xright + yleft));
|
|||
|
|
double k3 = sin(pi * (xleft + yright));
|
|||
|
|
double k4 = sin(pi * (xleft + yleft));
|
|||
|
|
fluids[index].primvar[0] = 1.0 - 0.2 / pi / pi / block.dx / block.dy * ((k1 - k2) - (k3 - k4));
|
|||
|
|
|
|||
|
|
fluids[index].primvar[1] = 1;
|
|||
|
|
fluids[index].primvar[2] = 1;
|
|||
|
|
fluids[index].primvar[3] = 1;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
#pragma omp parallel for
|
|||
|
|
for (int i = block.ghost; i < block.nx - block.ghost; i++)
|
|||
|
|
{
|
|||
|
|
for (int j = block.ghost; j < block.ny - block.ghost; j++)
|
|||
|
|
{
|
|||
|
|
int index = i * (block.ny) + j;
|
|||
|
|
Primvar_to_convar_2D(fluids[index].convar, fluids[index].primvar);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
void error_for_sinwave_2d(Fluid2d* fluids, Block2d block, double tstop, double* error)
|
|||
|
|
{
|
|||
|
|
if (abs(block.t - tstop) <= (1e-10))
|
|||
|
|
{
|
|||
|
|
cout << "Accuracy-residual-file-output" << endl;
|
|||
|
|
double error1 = 0;
|
|||
|
|
double error2 = 0;
|
|||
|
|
double error3 = 0;
|
|||
|
|
for (int i = block.ghost; i < block.nx - block.ghost; i++)
|
|||
|
|
{
|
|||
|
|
for (int j = block.ghost; j < block.ny - block.ghost; j++)
|
|||
|
|
{
|
|||
|
|
double pi = 3.14159265358979323846;
|
|||
|
|
int index = i * block.ny + j;
|
|||
|
|
double xleft = (i - block.ghost) * block.dx;
|
|||
|
|
double xright = (i + 1 - block.ghost) * block.dx;
|
|||
|
|
double yleft = (j - block.ghost) * block.dy;
|
|||
|
|
double yright = (j + 1 - block.ghost) * block.dy;
|
|||
|
|
|
|||
|
|
//case in two dimensional x-y-plane
|
|||
|
|
double k1 = sin(pi * (xright + yright));
|
|||
|
|
double k2 = sin(pi * (xright + yleft));
|
|||
|
|
double k3 = sin(pi * (xleft + yright));
|
|||
|
|
double k4 = sin(pi * (xleft + yleft));
|
|||
|
|
double primvar0 = 1.0 - 0.2 / pi / pi / block.dx / block.dy * ((k1 - k2) - (k3 - k4));
|
|||
|
|
|
|||
|
|
|
|||
|
|
error1 = error1 + abs(fluids[index].convar[0] - primvar0);
|
|||
|
|
error2 = error2 + pow(fluids[index].convar[0] - primvar0, 2);
|
|||
|
|
error3 = (error3 > abs(fluids[index].convar[0] - primvar0)) ? error3 : abs(fluids[index].convar[0] - primvar0);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
error1 /= (block.nodex * block.nodey);
|
|||
|
|
error2 = sqrt(error2 / (block.nodex * block.nodey));
|
|||
|
|
error[0] = error1; error[1] = error2; error[2] = error3;
|
|||
|
|
}
|
|||
|
|
}
|