class
TransportProblemShearDiffContents
 Reference
Transport PDE problem: diffusion of a shear layer
This class implements the analytical solutions for the test problem, adopted from Okubo Akira Karweit Michael J. , (1969), DIFFUSION FROM A CONTINUOUS SOURCE IN A UNIFORM SHEAR FLOW, Limnology and Oceanography, 14, doi: 10.4319/lo.1969.14.4.0514. In essence, this is a test problem for the advectiondiffusion equation in 3D where the analytical solution is known in a closed form as the solution evolves in time. The initial solution is a Gaussian that is advected and diffused in time with an imposed constantintime velocity field that features advection and shear. Also, the diffusion coefficients can be different in the three coordinate directions. Note that t0 as well as all three components of the diffusion must be larger than zero at t=t0 to have a welldefined initial condition.
In a nutshell, the equation solved is
whose solution is given by
where . See also the paper.
Public static functions

static auto initialize(ncomp_
t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real z, tk::real t) > std::vector<tk::real >  Initialize numerical solution.

static auto analyticSolution(ncomp_
t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real z, tk::real t) > std::vector<tk::real >  Evaluate analytical solution at (x,y,z,t) for all components.

static auto prescribedVelocity(ncomp_
t system, ncomp_t ncomp, tk::real , tk::real y, tk::real z, tk::real ) > std::vector<std::array<tk::real , 3>>  Assign prescribed shear velocity at a point.

static auto type() > ctr::
ProblemType noexcept  Return problem type.
Public functions
Function documentation
static std::vector<tk::real > inciter::TransportProblemShearDiff:: initialize(ncomp_t system,
ncomp_t ncomp,
tk::real x,
tk::real y,
tk::real z,
tk::real t)
Initialize numerical solution.
Parameters  

system in  Equation system index 
ncomp in  Number of components in this transport equation system 
x in  X coordinate where to evaluate the solution 
y in  Y coordinate where to evaluate the solution 
z in  Z coordinate where to evaluate the solution 
t in  Time where to evaluate the solution 
Returns  Values of all components evaluated at (x,y,t) 
static std::vector<std::array<tk::real , 3>> inciter::TransportProblemShearDiff:: prescribedVelocity(ncomp_t system,
ncomp_t ncomp,
tk::real ,
tk::real y,
tk::real z,
tk::real )
Assign prescribed shear velocity at a point.
Parameters  

system in  Equation system index, i.e., which transport equation system we operate on among the systems of PDEs 
ncomp in  Number of components in this transport equation 
y in  y coordinate at which to assign velocity 
z in  Z coordinate at which to assign velocity 
Returns  Velocity assigned to all vertices of a tetrehedron, size: ncomp * ndim = [ncomp][3] 
void inciter::TransportProblemShearDiff:: errchk(ncomp_t system,
ncomp_t ncomp) const
Do error checking on PDE parameters.
Parameters  

system in  Equation system index, i.e., which transport equation system we operate on among the systems of PDEs 
ncomp in  Number of components in this transport equation 