Each case gives the test definition, boundary-condition configuration, mesh size, validation basis, result summary and the related plots or solution field.
Conservation, compressible-flow and solid-conduction benchmarks.
A closed uniform-flow problem used to verify that the discretization does not generate a solution when every boundary flux is zero.
Zero normal mass, momentum and energy flux on the external boundaries; uniform initial state.
500 cells
The exact solution is the unchanged initial field.
The density remains 1.0 across the domain.
An axisymmetric shock-tube problem containing an expansion wave, contact discontinuity and shock.
Axis condition on the centreline; two initial states separated by a diaphragm discontinuity; transient shock-tube end boundaries.
500 cells
Density, velocity, pressure and internal energy are compared with the reference Riemann solution.
CMPS reproduces the principal wave locations and plateau states.
Two-dimensional steady supersonic flow over a 15-degree ramp, producing an attached oblique shock.
Supersonic inflow; solid ramp wall; supersonic outlet and outer far-field boundary.
165,000 cells
Analytical post-shock reference values: temperature 382.0, density 2.277 and Mach 1.874.
CMPS gives 377.7617, 2.2310 and 1.8983 respectively; differences are approximately 1.11%, 2.02% and 1.30%.
A steady supersonic nozzle flow containing an internal normal shock.
Supersonic nozzle inlet; solid nozzle walls; downstream outlet condition selected to sustain an internal normal shock.
8,000 cells
The axial Mach-number distribution is compared with the analytical nozzle and normal-shock solution.
CMPS follows the analytical acceleration and the abrupt transition through the shock.
A centred two-dimensional expansion of inviscid supersonic flow around a corner.
Supersonic inlet; slip walls forming the expansion corner; supersonic outlet and far-field boundary.
8,154 cells
The downstream Mach number is compared with the analytical Prandtl-Meyer value of 3.237.
CMPS gives Mach 3.1896, a difference of approximately 1.46%.
One-dimensional steady heat conduction configured axisymmetrically.
Prescribed temperatures at the thermal boundaries; axis condition on the centreline; remaining surfaces insulated or symmetric.
500 cells
The temperature distribution is compared with the steady analytical conduction profile.
The computed temperature profile follows the reference linear distribution.
One-dimensional steady solid conduction with a constant heat-flux boundary, configured axisymmetrically.
Specified wall heat flux; thermal reference condition on the opposite boundary; axis condition on the centreline.
500 cells
The temperature distribution is compared with the analytical constant-heat-flux solution.
CMPS reproduces the expected temperature gradient through the solid.
Every row includes its wall condition, mesh and the related validation figure.
| Official test name | Boundary conditions and mesh | Validation result | Plots and field |
|---|---|---|---|
| Laminar Flat Plate (Adiabatic) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip adiabatic plate wall.Mesh4,096 cells | Skin-friction and velocity profiles follow the laminar analytical correlations. |  |
| Laminar Flat Plate (Cons T) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip constant-temperature plate wall.Mesh3,136 cells | Skin friction, wall heat flux and velocity follow the reference distributions. |  |
| Laminar Flat Plate (Cons HF) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip constant-heat-flux plate wall.Mesh3,136 cells | Skin friction, thermal wall response and velocity follow the analytical trends. |  |
| Turbulent Flat Plate (Adiabatic) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip adiabatic wall; near-wall resolution around y+ = 1.Mesh13,464 cells | CMPS captures the reference skin-friction trend and nondimensional near-wall velocity behaviour. |  |
| Turbulent Flat Plate (Const T) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip constant-temperature plate wall.Mesh13,056 cells | Skin friction, heat flux and velocity follow the turbulent reference relations. |  |
| Turbulent Flat Plate (Const HF) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip constant-heat-flux plate wall.Mesh13,056 cells | Skin friction, wall temperature and velocity show the expected aerodynamic and thermal development. |  |
| Turbulent Flat Plate (Adiabatic y+) Test Case | Boundary conditionsFreestream inlet and far-field; downstream outlet; no-slip adiabatic wall with several first-cell spacings.Mesh13,464 cells for y+ = 1, 3 and 20; 10,744 cells for y+ = 110 | Skin-friction curves show the wall-treatment response across the tested y+ values. |  |
| Laminar Flat Plate (Adiabatic SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip adiabatic plate wall.Mesh25,000 cells | Skin friction, wall temperature and near-cell temperature follow compressible reference correlations. |  |
| Laminar Flat Plate (ConstT SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip constant-temperature plate wall.Mesh25,000 cells | Skin friction, heat flux and near-cell temperature track the compressible reference curves. |  |
| Laminar Flat Plate (ConstHF SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip constant-heat-flux plate wall.Mesh25,000 cells | CMPS follows the reference skin-friction, wall-temperature and near-cell-temperature profiles. |  |
| Turbulent Flat Plate (Adiabatic SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip adiabatic wall at approximately y+ = 16.Mesh25,000 cells | CMPS captures the compressible turbulent skin-friction and recovery-temperature response. |  |
| Turbulent Flat Plate (Cons T SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip constant-temperature wall at approximately y+ = 16.Mesh25,000 cells | Skin friction, heat flux and near-cell temperature follow the compressible reference relations. |  |
| Turbulent Flat Plate (Cons HF SS) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip constant-heat-flux wall at approximately y+ = 16.Mesh25,000 cells | CMPS follows the expected compressible aerodynamic and thermal development. |  |
| Turbulent Flat Plate (Adiabatic SS y+) Test Case | Boundary conditionsSupersonic freestream inlet and far-field; supersonic outlet; no-slip adiabatic wall with y+ from 1 to 256.Mesh25,000 cells for each y+ subcase | The skin-friction comparison shows the consistency and limits of the compressible wall treatment across the y+ sweep. |  |
Direct comparisons with wind-tunnel or laboratory measurements.
An axisymmetric HB-2 external-aerodynamics benchmark at Mach 3.
Mach-3 supersonic far-field; axis condition on the centreline; body wall; downstream far-field or outlet.
13,761 cells
The drag coefficient is compared with the published wind-tunnel correlation.
The CMPS Mach-3 point lies close to the measured drag trend.
A two-dimensional turbulent transonic external-flow benchmark around the RAE2822 airfoil.
Transonic far-field around the airfoil; no-slip airfoil wall; downstream and outer pressure far-field boundary.
20,061 cells
The surface aerodynamic distribution is compared directly with RAE2822 wind-tunnel measurements.
CMPS reproduces the measured surface trend and the transonic shock region.
A steady turbulent compressible mixing layer between two streams with different velocities.
Two inlet streams; upper and lower free-stream boundaries; downstream outlet.
10,800 cells
The transverse velocity profile is compared with the Goebel-Dutton experiment.
CMPS captures the measured velocity transition and shear-layer location.
A two-dimensional Burrows-Kurkov supersonic mixing benchmark; the inert-gas configuration is used for validation.
Separate vitiated-air and inert-gas inlet streams; duct walls; downstream outlet.
17,180 cells
H2, N2 and H2O mass-fraction profiles, together with the reported total-temperature measurements.
The CMPS species profiles reproduce the measured mixing development.
A SCRAMJET-exhaust representation in which a supersonic jet produces a reflected shock over an afterbody.
Supersonic nozzle or exhaust inlet; constant-temperature afterbody wall; external far-field or outlet; mixture and multispecies formulations.
29,000 cells for the mixture case; 49,960 cells for the multispecies case.
Only the measured pressure distribution is used. Heat transfer is excluded because it was not evaluated with the constant-temperature wall setup.
Both formulations reproduce the principal measured pressure rise associated with shock reflection.
A two-dimensional steady turbulent dispersed-particle flow over a backward-facing step.
Carrier-flow and particle inlet; no-slip channel and step walls; downstream outlet; coupled dispersed-phase transport.
30,000 cells
Particle-velocity profiles are compared with measurements at x = 0.225, 0.275, 0.375 and 0.425.
CMPS captures the measured particle acceleration and recovery through the separated-flow region.
