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transport_tensor_exact.icc
Go to the documentation of this file.
point u(const point& x) { return point (-x[1], x[0]); }
tensor grad_u = {{0,-1},{1,0}};
struct sigma_exact {
Float f (const point& x) const {
return 0.5*exp( - nu*t - norm2(x-xt)/sqr(r0));
}
Float df_dt (const point& x) const {
return ( - nu + 2*dot(vt,x-xt)/sqr(r0))*f(x);
}
tensor operator() (const point& x) const {
Float c0 = f(x);
tensor s;
s(0,0) = c0*(1+cos(2*t));
s(1,1) = c0*(1-cos(2*t));
s(0,1) =
s(1,0) = c0*sin(2*t);
return s;
}
tensor time_derivative (const point& x) const {
Float c0 = f(x);
Float c1 = df_dt(x);
tensor s;
s(0,0) = c1*(1+cos(2*t)) - 2*c0*sin(2*t);
s(1,1) = c1*(1-cos(2*t)) + 2*c0*sin(2*t);
s(0,1) =
s(1,0) = c1*sin(2*t) + 2*c0*cos(2*t);
return s;
}
sigma_exact (Float nu1, Float t1 = 0)
: nu(nu1), t(t1), r0(0.1), x0(0.25,0), xt(), vt()
{
xt = point( x0[0]*cos(t) - x0[1]*sin(t),
x0[0]*sin(t) + x0[1]*cos(t));
vt = point(-x0[0]*sin(t) - x0[1]*cos(t),
x0[0]*cos(t) - x0[1]*sin(t));
}
Float nu, t, r0;
point x0, xt, vt;
};
struct chi {
tensor operator() (const point& x) const {
return - _s.time_derivative(x);
}
chi (Float nu, Float t = 0): _s(nu, t) {}
sigma_exact _s;
};
typedef sigma_exact sigma_g;
Float
see the Float page for the full documentation
point
see the point page for the full documentation
tensor
see the tensor page for the full documentation
sigma_g
sigma_exact sigma_g
Definition diffusion_tensor_exact.icc:50
chi
Definition diffusion_tensor_exact.icc:38
chi::operator()
tensor operator()(const point &x) const
Definition diffusion_tensor_exact.icc:39
chi::_s
sigma_exact _s
Definition diffusion_transport_tensor_exact.icc:86
chi::chi
chi(Float nu, Float t=0)
Definition transport_tensor_exact.icc:69
f
Definition cavity_dg.h:29
grad_u
Definition combustion_exact.icc:34
nu
Definition nu.h:26
sigma_exact
Definition diffusion_tensor_exact.icc:25
sigma_exact::xt
point xt
Definition diffusion_transport_tensor_exact.icc:78
sigma_exact::operator()
tensor operator()(const point &x) const
Definition diffusion_tensor_exact.icc:26
sigma_exact::f
Float f(const point &x) const
Definition transport_tensor_exact.icc:29
sigma_exact::df_dt
Float df_dt(const point &x) const
Definition transport_tensor_exact.icc:32
sigma_exact::t
Float t
Definition diffusion_transport_tensor_exact.icc:77
sigma_exact::x0
point x0
Definition diffusion_transport_tensor_exact.icc:78
sigma_exact::time_derivative
tensor time_derivative(const point &x) const
Definition transport_tensor_exact.icc:44
sigma_exact::vt
point vt
Definition diffusion_transport_tensor_exact.icc:78
sigma_exact::sigma_exact
sigma_exact(Float nu1, Float t1=0)
Definition transport_tensor_exact.icc:54
sigma_exact::nu
Float nu
Definition diffusion_transport_tensor_exact.icc:77
sigma_exact::r0
Float r0
Definition diffusion_transport_tensor_exact.icc:77
u
Definition leveque.h:25