cut_cell_closure.hpp

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#ifndef PECLET_CORE_SCHEME_CUT_CELL_CLOSURE_HPP
#define PECLET_CORE_SCHEME_CUT_CELL_CLOSURE_HPP
 
#ifdef KOKKOS_INLINE_FUNCTION
#define PECLET_CORE_CC_HD KOKKOS_INLINE_FUNCTION
#else
#define PECLET_CORE_CC_HD inline
#endif
 
namespace peclet::core::scheme {
 
// ---- boundary-distance polynomials, SCHEME 0 (point-value) ----
template <class Real>
PECLET_CORE_CC_HD Real poly_D(Real xi) {
  return xi * (Real(1) + xi);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_N_nb(Real xi) {
  return xi * (Real(1) - xi);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nc(Real xi) {
  return Real(2) * (xi * xi - Real(1));
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc(Real) {
  return Real(2);
}
 
// ---- SCHEME 1 (cell-average) siblings ----
template <class Real>
PECLET_CORE_CC_HD Real poly_D_avg(Real xi) {
  return xi * (Real(1) + xi) - Real(1) / Real(12);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nnb_avg(Real xi) {
  return xi * (Real(1) - xi) + Real(1) / Real(12);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nc_avg(Real xi) {
  return Real(2) * (xi * xi - Real(1)) - Real(1) / Real(6);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc_avg(Real) {
  return Real(2);
}
 
// ---- Navier-slip generalization of the SCHEME 0 polynomials (flow WO-V6b; amr does not use
// these -- point-shell wall models are a flow/dem convention). See flow/src/cut_cell_ibm.hpp for
// the derivation (P = theta + lam, Q = theta^2 + 2*lam*theta); lam = 0 reproduces poly_D /
// poly_N_nb / poly_Nc identically.
template <class Real>
PECLET_CORE_CC_HD Real poly_D_slip(Real xi, Real lam) {
  return poly_D(xi) + lam * (Real(1) + Real(2) * xi);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_N_nb_slip(Real xi, Real lam) {
  return poly_N_nb(xi) + lam * (Real(1) - Real(2) * xi);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nc_slip(Real xi, Real lam) {
  return poly_Nc(xi) + Real(4) * lam * xi;
}
 
// ---- sandwiched axis (both neighbours solid = a one-cell fluid gap), SCHEME 0 then SCHEME 1 ----
template <class Real>
PECLET_CORE_CC_HD Real poly_D_sandwich(Real xi_m, Real xi_p) {
  return xi_m * xi_p;
}
template <class Real>
PECLET_CORE_CC_HD Real poly_N_c_sandwich(Real xi_m, Real xi_p) {
  return (xi_m + Real(1)) * (xi_p - Real(1));
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc_pp_sw(Real xi_m, Real xi_p) {
  return (xi_m / (xi_m + xi_p)) * (Real(1) + xi_m);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc_mp_sw(Real xi_m, Real xi_p) {
  return (xi_p / (xi_m + xi_p)) * (Real(1) - xi_p);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_D_sandwich_avg(Real xi_m, Real xi_p) {
  return xi_m * xi_p - Real(1) / Real(12);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_N_c_sandwich_avg(Real xi_m, Real xi_p) {
  return (xi_m + Real(1)) * (xi_p - Real(1)) - Real(1) / Real(12);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc_pp_sw_avg(Real xi_m, Real xi_p) {
  return (xi_m / (xi_m + xi_p)) * (Real(1) + xi_m) - Real(1) / Real(12);
}
template <class Real>
PECLET_CORE_CC_HD Real poly_Nbc_mp_sw_avg(Real xi_m, Real xi_p) {
  return (xi_p / (xi_m + xi_p)) * (Real(1) - xi_p) + Real(1) / Real(12);
}
 
}  // namespace peclet::core::scheme
 
#endif  // PECLET_CORE_SCHEME_CUT_CELL_CLOSURE_HPP