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Fundamental Curves Tab

The Fundamental Curves tab contains commands and settings for rarefaction, shock, and composite curves. These curves require a starting point, called a reference state, which is usually chosen by clicking in a point in the State Space window. They also depend on the choice of family, namely slow or fast. Curves are colored according to their family (blue for slow and red for fast).

Fundamental Curves Commands

Buttons that invoke commands related to fundamental curves

  • Integral Curve: Plot the integral curve of the line field associated to the specified family that goes through the chosen reference state. An integral curve stops if it hits the coincidence locus or the boundary, but not at the inflection locus.

  • Rarefaction Curve: Plot the rarefaction curve of the specified family that starts at the chosen reference state. Arrows point in the direction of increase of the characteristic speed. A rarefaction curve stops if it hits the inflection locus, the coincidence locus, or the boundary.

  • Rarefaction Flow: Fill State Space with many integral curves of the specified family. At least one curve goes through each cell on a rectangular grid. Viewed in a Wave Manifold window, these curves sketch out the Characteristic Manifold.

  • Shock Curve: Plot the shock curve of the specified family that starts at the chosen reference state. The shock curve, which is drawn as a dashed curve, depends also on the chosen sense, namely forward or backward: if the sense is forward, then the reference state is the left state of the shock wave, and vice versa. A shock curve stops at a certain type of sonic surface or at the boundary.

  • Shock Connection Verifier: Plot the connecting orbit for the shock wave chosen on a shock curve. After creating a shock curve, a shock wave can be chosen by clicking on (or near) the shock curve; the nearest point on the shock curve is taken as the opposite state of the shock wave, meaning the right state if the sense is forward, and vice versa.

TODO: Expand on the following.

  • Unclassified Rarefaction Curve Extension: Plot a rarefaction curve and its unclassified extension.

  • Rarefaction Curve Extension: Plot a rarefaction curve and its extension.

  • Composite Curve: Plot a composite curve and its rarefaction base curve.

  • Composite Connection Verifier: Plot the connecting orbit for the composite wave chosen on a composite curve.

Fundamental Curve Settings

Fundamental curve calculation command configuration

  • Rarefaction Flow Resolution: Set the grid resolution

Raref. Settings

Rarefaction curve calculation command configuration

  • Sense: Choose the type of reference state of the rarefaction curve

    • Forward: The reference state is the left state of the rarefaction wave

    • Backward: The reference state is the right state of the rarefaction wave

  • Rarefaction Curve Attributes: See below.

Shock Settings

Shock curve calculation command configuration

  • Signs Choice:

  • Stepwise Verify Connection:

  • Shock Curve Attributes: See below.

Composite Settings

Composite curve calculation command configuration

  • Composite Curve Attributes: See below.

Rarefaction Orbit Configuration

  • Rarefaction ODE Integrator: integration method used to construct orbits

  • Rarefaction Relative Tolerance

  • Rarefaction Absolute Tolerance

  • Rarefaction Stepping Mode:

  • Rarefaction Step Size

  • Rarefaction Target Distance

  • Rarefaction Min Norm Increment (squared)

  • Rarefaction Min Norm RHS

  • Rarefaction Max Integration Steps

  • Rarefaction Arrow Size

  • Rarefaction Arrow Spacing

Curve Attributes

  • Color: Indicate classification type using colors

  • Arrows: Indicate the direction of speed change using arrows

  • Markers: Mark points where a chang in classification type occurs

  • Text: Annotate with text

  • Line: draw curves as solid, dashed, or dotted rather than as square dots

TODO: The following is for TESTING only.

  • Remove it as soon as possible.

  • Test of an internal link [Integral Curve][].

  • Notice that there is no need for a parenthesized URI, such as Shock Curve Attributes.

  • The reason is that this file contains no LaTeX, so that it can be compiled using pandoc.