HWENO fortran 代码

这是一个简单的HWENO（High-Order Weighted Essentially Non-Oscillatory）Fortran代码示例：

subroutine HWENO(u, uHWENO, N, dx)
  implicit none
  integer, intent(in) :: N
  real, intent(in) :: dx
  real, dimension(0:N-1), intent(in) :: u
  real, dimension(0:N-1), intent(out) :: uHWENO
  real, dimension(5) :: alpha
  real, dimension(5) :: w
  real, dimension(5) :: uL
  real, dimension(5) :: uR
  real :: eps = 1e-6
  integer :: i

  do i = 2, N-3
    alpha = [1/10.0, 6/10.0, 3/10.0, 0.0, 0.0]
    w = alpha / (eps + (u(i-2:i+2)-u(i))**2)
    w = w / sum(w)
    uL = [u(i-2), u(i-1), u(i), u(i+1), u(i+2)]
    uR = [u(i-1), u(i), u(i+1), u(i+2), u(i+3)]
    uHWENO(i) = w(1)*(-uL(1)+5*uL(2)+2*uL(3))/6.0 &
              + w(2)*(2*uL(2)+5*uL(3)-uL(4))/6.0 &
              + w(3)*(2*uL(3)+5*uL(2)-uL(1))/6.0 &
              + w(4)*(11*uL(3)-7*uL(2)+2*uL(1))/6.0 &
              + w(5)*(11*uL(3)-13*uL(2)+5*uL(1))/6.0
  end do

  uHWENO(0) = u(0)
  uHWENO(1) = u(1)
  uHWENO(N-2) = u(N-2)
  uHWENO(N-1) = u(N-1)

end subroutine HWENO

其中，`u`是输入的原始数据，`uHWENO`是输出的经过HWENO处理后的数据，`N`是数据点数，`dx`是网格间距。该代码使用了五阶HWENO格式来计算每个内部网格点的值，边界点直接复制原始数据的值。