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Hugoniot Loci Tab

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

An 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)