fluidity详解

1.fluidity编译过程

1.1.femtools库调用方法

1. 编译fluidity/femtools目录下所有文件，打包为libfemtools.a静态库文件；
2. 通过-lfemtools参数，并指定libfemtools.a静态库位置，即可调用 femtools 库内所有函数

2.fluidity主函数位置

fluidity可执行文件有4个，分别为：

1. fluidity
2. Burgers_Equation
3. Hybridized_Helmholtz_Solver
4. Shallow_Water

其中，Burgers_Equation、Hybridized_Helmholtz_Solver、Shallow_Water主程序源文件都在文件夹./main内，分别为./main/Burgers_Equation.F90，./main/Hybridized_Helmholtz_Solver.F90，./main/Shallow_Water.F90。

fluidity可执行文件源程序为最外层文件./main.cpp，main()函数则通过调用mainfl()函数来进行计算：

 // Start fortran mainif(fl_command_line_options.count("simulation_name")){mainfl();    }else{usage(argv[0]);exit(-1);}

mainfl()源程序位置为./main/mainfl.F90，主要调用fluids()函数：

     !######################################################!      Normal Fluidity Model!######################################################call tic(TICTOC_ID_SIMULATION)ewrite(1, *) "Calling fluids from mainfl"call fluids()ewrite(1, *) "Exited fluids"call toc(TICTOC_ID_SIMULATION)call tictoc_report(2, TICTOC_ID_SIMULATION)

fluids()函数源程序位置为./main/Fluids.F90

编译fluidity可执行文件函数调用顺序为main.cpp =>./main/mainfl.F90 =>./main/Fluids.F90

3.fluidity数据结构

fluidity数据结构层次：

下层数据(quadrature_type、element_type、mesh_type)构成上层数据(element_type、mesh_type、scalar_field、vector_field、tensor_field)类型基本元素，最上层为fluidity使用的标量、矢量、矩阵等数据类型。
下面逐个介绍基本数据类型：

3.1.quadrature_type

  type quadrature_type!!< A data type which describes quadrature information. For most!!< developers, quadrature can be treated as an opaque data type which!!< will only be encountered when creating element_type variables to!!< represent shape functions.  integer :: dim !! Dimension of the elements for which quadrature!!< is required.  integer :: degree !! Degree of accuracy of quadrature. integer :: vertices !! Number of vertices of the element.integer :: ngi !! Number of quadrature points.real, pointer :: weight(:)=>null() !! Quadrature weights.real, pointer :: l(:,:)=>null() !! Locations of quadrature points.character(len=0) :: name !! Fake name for reference counting.!! Reference count to prevent memory leaks.type(refcount_type), pointer :: refcount=>null()integer :: familyend type quadrature_type

quadrature_type包含了基本单元信息，包括

1. dim 维度
2. degree 多项式阶数
3. vertices 节点个数
4. ngi 正交节点个数
5. weight(:) 权重
6. l(:,:) 正交节点位置
7. name
8. refcount
9. family

这些信息都是构成基本单元层面的。

    !!< Given information about a quadrature, return a quad type encoding!!< that quadrature.function make_quadrature(vertices, dim, degree, ngi, family, stat) result (quad)integer :: lfamilyinteger :: wandzura_rule_idx, wandzura_rule_degree, max_wandzura_rule, wandzura_orderreal, dimension(2, 3) :: wandzura_ref_trireal, dimension(3, 3) :: wandzura_ref_mapreal, dimension(:, :), allocatable :: tmp_coordinatesinteger :: giinteger :: gm_rule, gm_order, vertexreal, dimension(:, :), allocatable :: gm_ref_simplexreal, dimension(:, :), allocatable :: gm_ref_mapif (present(family)) thenlfamily = familyelselfamily = FAMILY_COOLSend iffamily_if: if (lfamily == FAMILY_COOLS) then

下面根据lfamily取值对quad进行赋值，lfamily三个值分别为

1. FAMILY_COOLS = 0
2. FAMILY_WANDZURA = 1
3. FAMILY_GM = 2

family_if: else if (lfamily == FAMILY_WANDZURA) then! Make sure we're on triangles.if (dim /= 2 .or. vertices /= 3) thenwrite (quadrature_error_message, '(a,i0,a)') ...end if! OK. First let's figure out which rule we want to use.if (.not. present(degree)) thenwrite (quadrature_error_message, '(a,i0,a)') ...end ifcall wandzura_rule_num(max_wandzura_rule)do wandzura_rule_idx=1,max_wandzura_rulecall wandzura_degree(wandzura_rule_idx, wandzura_rule_degree)  !! degree=idx*5if (wandzura_rule_degree >= degree) exit !! 当Wandzura精度超过指定精度后跳出循环end doif (wandzura_rule_degree < degree) then !! 循环结束后Wandzura最大精度为30，指定精度不能超过30write error message ..end ifcall wandzura_order_num(wandzura_rule_idx, wandzura_order)!! 获得 wandzura_order(三角形单元中节点总个数) = ngicall allocate(quad, vertices, wandzura_order, coords=3)allocate(tmp_coordinates(2, wandzura_order))quad%degree = wandzura_rule_degreequad%dim = 2call wandzura_rule(wandzura_rule_idx, wandzura_order, tmp_coordinates, quad%weight)!! 获得 wandzura 节点坐标 tmp_coordinates；积分权重 quad%weightwandzura_ref_tri(:, 1) = (/0, 0/)wandzura_ref_tri(:, 2) = (/1, 0/)wandzura_ref_tri(:, 3) = (/0, 1/)call local_coords_matrix_positions(wandzura_ref_tri, wandzura_ref_map)do gi=1,wandzura_orderquad%l(gi, 1:2) = tmp_coordinates(:, gi); quad%l(gi, 3) = 1.0quad%l(gi, :) = matmul(wandzura_ref_map, quad%l(gi, :))end do

在这之中有个重要的子函数调用，call allocate(quad, vertices, wandzura_order, coords=3)，目的就是为结构体quad申请内存空间。下面检查下子函数allocate的内容，

    interface allocatemodule procedure allocate_quadend interface......subroutine allocate_quad(quad, vertices, ngi, coords, stat)allocate(quad%weight(ngi), quad%l(ngi,coords), stat=lstat)quad%vertices=verticesquad%ngi=nginullify(quad%refcount)call addref(quad)end subroutine allocate_quad

剩下最后一种定义quad方式：FAMILY_GM

    family_if:elseif (lfamily == FAMILY_GM) then......family_if:else......family_if:end if......quad%family = lfamilyend function make_quadrature`

3.2.element_type

  type element_type!!< Type to encode shape and quadrature information for an element.integer :: dim !! 2d or 3d?integer :: loc !! Number of nodes.integer :: ngi !! Number of gauss points.integer :: degree !! Polynomial degree of element.!! Shape functions: n is for the primitive function, dn is for partial derivatives, dn_s is for partial derivatives on surfaces. !! n is loc x ngi, dn is loc x ngi x dim!! dn_s is loc x ngi x face x dim real, pointer :: n(:,:)=>null(), dn(:,:,:)=>null()real, pointer :: n_s(:,:,:)=>null(), dn_s(:,:,:,:)=>null()!! Polynomials defining shape functions and their derivatives.type(polynomial), dimension(:,:), pointer :: spoly=>null(), dspoly=>null()!! Link back to the node numbering used for this element.type(ele_numbering_type), pointer :: numbering=>null()!! Link back to the quadrature used for this element.type(quadrature_type) :: quadraturetype(quadrature_type), pointer :: surface_quadrature=>null()!! Pointer to the superconvergence data for this element.type(superconvergence_type), pointer :: superconvergence=>null()!! Pointer to constraints data for this elementtype(constraints_type), pointer :: constraints=>null()!! Reference count to prevent memory leaks.type(refcount_type), pointer :: refcount=>null()!! Dummy name to satisfy reference countingcharacter(len=0) :: nameend type element_type

相较而言element_type就复杂了一点，

自定义类型：ele_numbering_type，与 polynomial

  type ele_numbering_type! Type to record element numbering details.! Differentiate tets from other elements.integer :: faces, vertices, edges, boundariesinteger :: degree ! Degree of polynomials.integer :: dimension ! 2D or 3Dinteger :: nodesinteger :: type=ELEMENT_LAGRANGIANinteger :: family! Map local count coordinates to local number.integer, dimension(:,:,:), pointer :: count2number! Map local number to local count coordinates.integer, dimension(:,:), pointer :: number2count! Count coordinate which is held constant for each element boundary.integer, dimension(:), pointer :: boundary_coord! Value of that count coordinate on the element boundary.integer, dimension(:), pointer :: boundary_valend type ele_numbering_type

    type polynomialreal, dimension(:), pointer :: coefs=>null()integer :: degree=-1end type polynomial

3.3.mesh_type

  type mesh_type!!< Mesh information for (among other things) fields.integer, dimension(:), pointer :: ndglno!! Flag for whether ndglno is allocatedlogical :: wrapped=.true.type(element_type) :: shapeinteger :: elementsinteger :: nodescharacter(len=FIELD_NAME_LEN) :: name!! path to options in the options tree
#ifdef DDEBUGcharacter(len=OPTION_PATH_LEN) :: option_path="/uninitialised_path/"
#elsecharacter(len=OPTION_PATH_LEN) :: option_path
#endif!! Degree of continuity of the field. 0 is for the conventional C0!! discretisation. -1 for DG.integer :: continuity=0!! Reference count for meshtype(refcount_type), pointer :: refcount=>null()!! Mesh face information for those meshes (eg discontinuous) which need it.type(mesh_faces), pointer :: faces=>null()!! Information on subdomain_ mesh, for partially prognostic solves:type(mesh_subdomain_mesh), pointer :: subdomain_mesh=>null()type(adjacency_cache), pointer :: adj_lists => null()!! array that for each node tells which column it is in!! (column numbers usually correspond to a node number in a surface mesh)integer, dimension(:), pointer :: columns => null()!! if this mesh is extruded this array says which horizontal mesh element each element is belowinteger, dimension(:), pointer :: element_columns => null()!! A list of ids marking different parts of the mesh!! so that initial conditions can be associated with it.integer, dimension(:), pointer :: region_ids=>null()!! Halo information for parallel simulations.type(halo_type), dimension(:), pointer :: halos=>null()type(halo_type), dimension(:), pointer :: element_halos=>null()type(integer_set_vector), dimension(:), pointer :: colourings=>null()!! A logical indicating if this mesh is periodic or not!! (does not tell you how periodic it is... i.e. true if!! any surface is periodic)logical :: periodic=.false.end type mesh_type

3.4.一维例子

test_1d.F90

    function read_triangle_simple(filename, quad_degree, quad_ngi, no_faces, quad_family, mdim) result (field)