zalesak_circle.h

The Zalesak full disk benchmark – the exact solution.

The Zalesak full disk benchmark – the exact solution

struct u {
  point operator() (const point& x) const {
    return point(-0.5*(x[1]-yc), 0.5*(x[0]-xc));
  }
  static Float period() {
    Float pi = acos (Float(-1));
    return 4*pi;
  }
  u() {}
protected:
  static constexpr Float
    xc = 0.5,  // rotation center
    yc = 0.5;
};
struct phi_exact {
  Float operator() (const point& x) const {
    Float xm = xr + cos(0.5*t)*(x[0]-xr) + sin(0.5*t)*(x[1]-yr);
    Float ym = yr - sin(0.5*t)*(x[0]-xr) + cos(0.5*t)*(x[1]-yr);
    return sqrt(sqr(xm-x0) + sqr(ym-y0)) - r;
  }
  Float perimeter() const { return 2*acos(Float(-1))*r; }
  phi_exact (float t1) : t(t1) {}
protected:
  Float t;
  static constexpr Float xr = 0.5,  // rotation center
                         yr = 0.5,
                         x0 = 0.50, // circle center
                         y0 = 0.75,
                         r  = 0.15;  // circle radius
};
struct phi0 {
  Float operator() (const point& x) const { return _phi(x); }
  phi0() : _phi(0) {}
  phi_exact _phi;
};