Shock Tube + YZB Discontinuity Capturing (#851)

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the

Shock Tube + YZB Discontinuity Capturing (#851)

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Changed variable name midpt to mid_point, removed redundant slip BC declarations.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Rebased with main

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Implemented fixes to the flux jacobians

* Updated documentation, tau definition in SU, and recommended fixes to the flux Jacobian.

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Missed a style fix

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixes to style and documentation.

* Fixing unnecessary problem->dim declaration and missing field in comment describing initial condition density.

* Added warnings for incompatible user input combinations.

* Added comments on beta to documentation, fixed j_gradn style issues.

* Compilation errors on my end. Committing to see if it's local or not.

* Style fixes

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Changed variable name midpt to mid_point, removed redundant slip BC declarations.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Rebased with main

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Implemented fixes to the flux jacobians

* Updated documentation, tau definition in SU, and recommended fixes to the flux Jacobian.

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Missed a style fix

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixes to style and documentation.

* Fixing unnecessary problem->dim declaration and missing field in comment describing initial condition density.

* Added warnings for incompatible user input combinations.

* Added comments on beta to documentation, fixed j_gradn style issues.

* Compilation errors on my end. Committing to see if it's local or not.

* Fluids: SETERRQ1 -> SETERRQ to be compatible with PETSc 3.17

* Fluids - Update shock-tube with #881

* Small fix to mid_point definition and removed repeat entries for Shock Tube problem in README.md.

* Including test output.

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Changed variable name midpt to mid_point, removed redundant slip BC declarations.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Rebased with main

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixed style error, made variable names clearer, and removed dead code.

* Missed a style fix

* Implemented fixes to the flux jacobians

* Updated documentation, tau definition in SU, and recommended fixes to the flux Jacobian.

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Missed a style fix

* Implemented the Sod Shock Tube problem with YZB discontinuity capturing. for the explicit formulation. SU stabilization is also implemented for the explicit formulation.

* Fixes to style and documentation.

* Fixing unnecessary problem->dim declaration and missing field in comment describing initial condition density.

* Added warnings for incompatible user input combinations.

* Added comments on beta to documentation, fixed j_gradn style issues.

* Compilation errors on my end. Committing to see if it's local or not.

* Fluids: SETERRQ1 -> SETERRQ to be compatible with PETSc 3.17

* Fluids - Update shock-tube with #881

* Fluids - added test output file for shocktube

* Small fix to mid_point definition and removed repeat entries for Shock Tube problem in README.md.

* Including test output.

* Update doc/sphinx/source/references.bib

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Update examples/fluids/README.md

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Update examples/fluids/index.md

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Update examples/fluids/navierstokes.h

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Update examples/fluids/problems/shocktube.c

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Update examples/fluids/qfunctions/shocktube.h

Co-authored-by: Jed Brown <jed@jedbrown.org>

* Removed unused IFunction

* Added shocktube variables to SetupContext in advection.h, advection2d.h, and densitycurrent.h

* Missed some merge conflicts that have now been cleared up.

* Added helper function for covariant element length along a given vector.

* Added SetupContext to shocktube.h

* Fix to regression test path

* remove variable transpose of the Jacobian

* Fix index swap in implicit SUPG

* examples/fluids shocktube: fix stab summation and transpose

* delete IFunction

* example/fluids- updates reference solution

Co-authored-by: Timothy Aiken <timothyaiken@Timothys-MacBook-Pro.local>
Co-authored-by: Timothy Aiken <timothyaiken@cu-biot-10-10.203.167.69.int.colorado.edu>
Co-authored-by: Leila Ghaffari <Leila.Ghaffari@colorado.edu>
Co-authored-by: Jed Brown <jed@jedbrown.org>
Co-authored-by: Timothy Aiken <timothyaiken@cu-genvpn-tcom-10.180.164.177.int.colorado.edu>
Co-authored-by: AdelekeBankole <adeleke.bankole@colorado.edu>

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