Struphy perturbation · physical basis

ManufacturedSolutionVelocity_2

Analytic solutions

u

and

u_{e}

of the system:

Governing formula

\partial_{t} u = - \nabla ϕ + u \times B + ν Δ u + f, 0 = \nabla ϕ - u_{e} \times B + ν_{e} Δ u_{e} + f_{e}, \nabla \cdot (u - u_{e}) = 0 .

Can only be defined in Cartesian coordinates. The solution in 1D is given by:

u = s in (2 π x) + 1.0 00, u_{e} = s in (2 π x) 00 .

The solution in 2D is given by:

u = - s in (2 π x) s in (2 π y) - cos (2 π y) cos (2 π y) 0, u_{e} = - s in (4 π x) s in (4 π y) - cos (4 π y) cos (4 π y) 0 .

The sampled perturbation value across the three logical coordinate planes.

Perturbation value ueta1–eta2 · 1.97e-3 to 2.00e+0

Perturbation value ueta1–eta3 · 1.97e-3 to 2.00e+0

Perturbation value ueta2–eta3 · 1.00e+0 to 1.00e+0

eta1 · other coordinates fixed at 0.5

eta2 · other coordinates fixed at 0.5

eta3 · other coordinates fixed at 0.5

Parameter	Value	Description
`species`	`Ions`	'Ions' or 'Electrons'.
`dimension`	`1D`	Defines the manufactured solution to be selected ('1D' or '2D').
`b0`	`1`	Magnetic field (default: 1.0).
`comp`	`0`	Which component (0, 1 or 2) of vector is perturbed (=0 for scalar-valued functions)