Struphy perturbation · physical basis

ManufacturedSolutionPotential

Analytic solution

ϕ

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 .

where $f$ is defined as follows:

f = [1 - b_{0} cos (x) - ν s in (y), 1 - b_{0} s in (y) + ν cos (x), 0], f_{e} = [- 1 + 0.5 b_{0} cos (x) - ν_{e} 0.5 s in (y), - 1 + 0.5 b_{0} s in (y) + ν_{e} cos (x), 0] .

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

ϕ = s in (2 π x) .

The solution in 2D is given by:

ϕ = cos (2 π x) + s in (2 π y) .

The sampled perturbation value across the three logical coordinate planes.

Perturbation value ueta1–eta2 · -9.98e-1 to 9.98e-1

Perturbation value ueta1–eta3 · -9.98e-1 to 9.98e-1

Perturbation value ueta2–eta3 · 1.22e-16 to 1.22e-16

eta1 · other coordinates fixed at 0.5

eta2 · other coordinates fixed at 0.5

eta3 · other coordinates fixed at 0.5

Parameter	Value	Description
`dimension`	`1D`	Defines the manufactured solution to be selected ('1D' or '2D').
`b0`	`1`	Magnetic field (default: 1.0).