The Spatio-Temporal Path system

[hugary1995]

close #116

This PR adds a new system associated with the syntax block [SpatioTemporalPaths]. Multiple SpatioTemporalPath-derived objects can be added under that syntax block. I have implemented 3 objects so far:

• PiecewiseLinearSpatioTemporalPath: This one accepts input file vectors t, x, y, z and constructs a spatio-temporal path object.
• CSVPiecewiseLinearSpatioTemporalPath: This one is similar to the previous one but instead reads from a csv file.
• FunctionSpatioTemporalPath: This one accepts moose functions for x, y and z.

Once a SpatioTemporalPath object is constructed, other MooseObjects can retrieve path given its name from the warehouse, through the SpatioTemporalPathInterface interface. See e.g. ADMovingHeatSource for how that coupling works.

Each spatio-temporal path objects recomputes several path-related information at every time step:

• SpatioTemporalPath::position() returns the current path front.
• SpatioTemporalPath::velocity() returns the current path moving velocity.
• SpatioTemporalPath::direction() returns the current path direction.

Variants of the above methods exist which accepts a time and computes the corresponding path information at the specified time.

By default the path-related information is recomputed at every time step, i.e. the path information is "live". The users have control over how often the path-related information is updated by the parameter update_interval. There are also methods that retrieve the path-related information from the previous update:

• SpatioTemporalPath::previousPosition()
• SpatioTemporalPath::previousVelocity()
• SpatioTemporalPath::previousDirection()

An object deriving from SpatioTemporalPath only need to override one single method Point position(Real t) const. Default implementations are provided for RealVectorValue velocity(Real t) and RealVectorValue direction(Real t) which use finite-differencing to compute the derivatives. The developer can optionally override these methods to provide more efficient/accurate implementations.

Utility methods are provided to compute the tangential and normal components of the distance between a given point and the path's current position.

• SpatioTemporalPath::tangentialDistance(const Point & p)
• SpatioTemporalPath::normalDistance(const Point & p)

Similarly, variants of the above methods exist which additionally accepts a specified time.

Spatio-temporal paths are useful in many scenarios. I have added two concrete examples for demonstration purposes:

• ADMovingHeatSource and ADMovingEllipsoidalHeatSource
• SpatioTemporalPathElementSubdomainModifier

Their names are self-explanatory. Note that ADMovingEllipsoidalHeatSource makes use of the tangential and normal distance to effectively "rotate" the ellipsoidal heat source.

[moosebuild]

Job Documentation on 554b071 wanted to post the following:

View the site here

This comment will be updated on new commits.

[moosebuild]

Job Coverage on 554b071 wanted to post the following:

Coverage

	d0e3c6	#117 554b07
	Total	Total	+/-	New
Rate	68.98%	71.41%	+2.43%	82.86%
Hits	1023	1284	+261	261
Misses	460	514	+54	54

Diff coverage report

Full coverage report

Warnings

• New new line coverage rate 82.86% is less than the suggested 90.0%

This comment will be updated on new commits.

[cticenhour]

Just took a look at the coverage diff - could you also add some error checking tests? The majority of the diff is missing coverage on mooseError calls.