# inciter::TransportProblemGaussHump class

Transport PDE problem: advection of two-dimensional Gaussian hump.

• Reference

## Public static functions

static auto solution(ncomp_t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real, tk::real t) -> std::vector<tk::real>
static auto solinc(ncomp_t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real, tk::real t, tk::real dt) -> std::vector<tk::real>
Evaluate the increment from t to t+dt of the analytical solution at (x,y,z) for all components.
static void errchk(
Do error checking on PDE parameters.
static void side(std::unordered_set<int>& conf)
Query all side set IDs the user has configured for all components in this PDE system.
static auto prescribedVelocity(ncomp_t, ncomp_t ncomp, tk::real, tk::real, tk::real) -> std::vector<std::array<tk::real, 3>>

## Function documentation

### static std::vector<tk::real> inciter::TransportProblemGaussHump::solution(ncomp_t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real, tk::real t)

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 system
in X coordinate where to evaluate the solution
in Y coordinate where to evaluate the solution
in Time where to evaluate the solution
Returns Values of all components evaluated at (x,y,t)

Evaluate analytical solution at (x,y,t) for all components

### static std::vector<tk::real> inciter::TransportProblemGaussHump::solinc(ncomp_t system, ncomp_t ncomp, tk::real x, tk::real y, tk::real, tk::real t, tk::real dt)

Evaluate the increment from t to t+dt of the analytical solution at (x,y,z) for all components.

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 system
in X coordinate where to evaluate the solution
in Y coordinate where to evaluate the solution
in Time where to evaluate the solution increment starting from
dt in Time increment at which evaluate the solution increment to
Returns Increment in values of all components evaluated at (x,y,t+dt)

### static void inciter::TransportProblemGaussHump::side(std::unordered_set<int>& conf)

Query all side set IDs the user has configured for all components in this PDE system.

Parameters
conf in/out Set of unique side set IDs to add to

### static std::vector<std::array<tk::real, 3>> inciter::TransportProblemGaussHump::prescribedVelocity(ncomp_t, ncomp_t ncomp, tk::real, tk::real, tk::real)

Parameters
ncomp in Number of components in this transport equation
Returns Velocity assigned to all vertices of a tetrehedron, size: ncomp * ndim = [ncomp]

Assign prescribed velocity at a point