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Hugoniot Loci Tab

The Hugoniot Loci Tab offers tools for creating and exploring the properties of a Hugoniot locus.

A shock wave is a discontinuity moving at speed \(\sigma\) and having constant state \(U^-\) on the left and constant state \(U^+\) on the right.

A Hugoniot locus is a set of shocks with one of its states fixed. The state that is fixed is called the reference state. If the reference state is \(U^-\), the Hugoniot is called a forward Hugoniot, whereas if the reference state is \(U^+\), it is called a backward Hugoniot.

TODO: Explain classification

Hugoniot commands

Buttons that invoke commands related to Hugoniot loci

  • Unclassified Hugoniot: Plot the Hugoniot curves without classification, with a single color

  • Hugoniot: Plot the Hugoniot curves with classification indicated by color

  • Hugoniot Classification: Show the classification of segments of a classified Hugoniot curve (click in a segment point and then in a place to print the rating)

  • Hugoniot Speeds: Show the shock speed associated with a segment of the Hugoniot curve

  • v = shock velocity

  • s = slow characteristic velocity

  • f = fast characteristic velocity

  • Change Point Type: Show change point classification. A zero indicates that the shock velocity equals the slow or fast characteristic velocity

Hugoniot Settings

Hugoniot curve calculation command configuration

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

  • Forward: The reference state is \(U^-\)

  • Backward: The reference state is \(U^+\)

  • Calculation Mode: Calculation method

  • General: Use a general numerical method, such as a contour plotter to solve the Rankine-Hugoniot equation as an implicit equation

  • Model: Use a model dependent numerical method, such as an analytical formula

  • Contour Algorithm: Choice of method for calculating the curve (GridValues is more efficient)

  • Swap States: Control the 3D projection

  • Speed Display Choices: Choose the speed information that will be shown

  • Shock Speed

  • Slow Characteristic Speed

  • Fast Characteristic Speed

  • Hugoniot Attributes: Indicate how to display the Hugoniot curve

  • Color: Show classification using colors

  • Arrows: Draw arrows indicating the direction of variation of wave speed

  • Squares: Mark the change points

  • Text: Show text indicating the reference state and sense

  • Line: Connect the points of the Hugoniot curve with line segments (it is sometimes helpful to draw the Hugoniot locus as a sequence of individual points)