[jcownbey]

I completed a simulation in SU2 on a supersonic 2D nozzle. I could only get a converged, realistic solution using a high CFL number (around 15). When I try to use a CFL number at 1 or below 1, the solution diverges or is unrealistic. Even in the tutorial on SU2's website with a convergent-divergent nozzle, the CFL number is high. Can someone explain why a high CFL number for an implicit solver is required to get a solution? Would solving the nozzle as time-accurate make a difference?

[pcg]

Maybe it is a matter of avoiding bad transients at the start of the simulation, what happens if you restart the simulation with lower CFL?
Higher CFL also tends to suppress or reduce limit-cycle-type behaviour, which is usually good when you want an average steady-state. In these cases however the residuals may not drop as much as they should, especially in the regions where that behaviour is being suppressed.

[jcownbey]

Running the simulation at a lower CFL causes the solution to diverge.

[pcg]

Are you using v6.2 or v7.0? This may be an important issue since in v7.0 significant changes were made to CFL-related areas of the code.
Can you attach the required files to reproduce the problem? mesh and configuration.

[jcownbey]

I am using v. 6.2. Do you know the changes made from 6.2 to 7.0? Or is there documentation on the changes? (besides the bullet points listed on the website).

The config file is posted below.

% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
% Physical governing equations (EULER, NAVIER_STOKES,
% FEM_EULER, FEM_NAVIER_STOKES, FEM_RANS, FEM_LES,
% WAVE_EQUATION, HEAT_EQUATION, FEM_ELASTICITY,
% POISSON_EQUATION)
PHYSICAL_PROBLEM= NAVIER_STOKES
MATH_PROBLEM= DIRECT % Mathematical problem (DIRECT, CONTINUOUS_ADJOINT, DISCRETE_ADJOINT)
REGIME_TYPE= COMPRESSIBLE % Regime type (COMPRESSIBLE, INCOMPRESSIBLE)
RESTART_SOL= NO % Restart solution (NO, YES)
SYSTEM_MEASUREMENTS= SI
KIND_TURB_MODEL= SST % Specify turbulence model (NONE, SA, SA_NEG, SST, SA_E, SA_COMP, SA_E_COMP)

% -------------------- COMPRESSIBLE FREE-STREAM DEFINITION --------------------%
MACH_NUMBER= 1E-9 % Mach number (non-dimensional, based on the free-stream values)
% Free-stream option to choose between density and temperature (default) for
% initializing the solution (TEMPERATURE_FS, DENSITY_FS)
FREESTREAM_OPTION= TEMPERATURE_FS
INIT_OPTION= TD_CONDITIONS
FREESTREAM_PRESSURE= 1888172.5755 % Free-stream pressure (101325.0 N/m^2, 2116.216 psf by default)
FREESTREAM_TEMPERATURE= 525.87 % Free-stream temperature (288.15 K, 518.67 R by default)
REF_DIMENSIONALIZATION= DIMENSIONAL

% ---- IDEAL GAS, POLYTROPIC, VAN DER WAALS AND PENG ROBINSON CONSTANTS -------%
% Fluid model (STANDARD_AIR, IDEAL_GAS, VW_GAS, PR_GAS,
% CONSTANT_DENSITY, INC_IDEAL_GAS, INC_IDEAL_GAS_POLY)
FLUID_MODEL= IDEAL_GAS
% Ratio of specific heats (1.4 default and the value is hardcoded
% for the model STANDARD_AIR, compressible only)
GAMMA_VALUE= 1.4
% Specific gas constant (287.058 J/kg*K default and this value is hardcoded
% for the model STANDARD_AIR, compressible only)
GAS_CONSTANT= 287.058

% --------------------------- THERMAL CONDUCTIVITY MODEL ----------------------%
% Laminar Conductivity model (CONSTANT_CONDUCTIVITY, CONSTANT_PRANDTL,
% POLYNOMIAL_CONDUCTIVITY).
CONDUCTIVITY_MODEL= CONSTANT_PRANDTL
PRANDTL_LAM= 0.72 % Laminar Prandtl number (0.72 (air), only for CONSTANT_PRANDTL)

% --------------------------- VISCOSITY MODEL ---------------------------------%
VISCOSITY_MODEL= CONSTANT_VISCOSITY % Viscosity model (SUTHERLAND, CONSTANT_VISCOSITY, POLYNOMIAL_VISCOSITY).
MU_CONSTANT= 1.716E-5 % Molecular Viscosity that would be constant (1.716E-5 by default)

% -------------------- BOUNDARY CONDITION DEFINITION --------------------------%
% Navier-Stokes (no-slip), constant heat flux wall marker(s) (NONE = no marker)
% Format: ( marker name, constant heat flux (J/m^2), ... )
MARKER_HEATFLUX= ( UPPER_WALL, 0.0, LOWER_WALL, 0.0 )
% Riemann boundary marker(s) (NONE = no marker)
% Format: (marker, data kind flag, list of data)
MARKER_RIEMANN= ( INFLOW, TOTAL_CONDITIONS_PT,1888172.5755, 525.87, 1.0, 0.0, 0.0, OUTFLOW, STATIC_PRESSURE, 101325, 0.0, 0.0, 0.0, 0.0)

% ------------------------ SURFACES IDENTIFICATION ----------------------------%
MARKER_PLOTTING = ( LOWER_WALL ) % Marker(s) of the surface in the surface flow solution file

% ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------%
NUM_METHOD_GRAD= GREEN_GAUSS % Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES)
CFL_NUMBER= 15 % CFL number (initial value for the adaptive CFL number)
CFL_ADAPT= NO % Adaptive CFL number (NO, YES)
RK_ALPHA_COEFF= ( 0.66667, 0.66667, 1.000000 ) % Runge-Kutta alpha coefficients
% Parameters of the adaptive CFL number (factor down, factor up, CFL min value,
% CFL max value )
CFL_ADAPT_PARAM= ( 1.5, 0.5, 0.0005, 15.0 )

% ----------- SLOPE LIMITER AND DISSIPATION SENSOR DEFINITION -----------------%
% Monotonic Upwind Scheme for Conservation Laws (TVD) in the flow equations.
% Required for 2nd order upwind schemes (NO, YES)
MUSCL_FLOW= YES
SLOPE_LIMITER_FLOW= VENKATAKRISHNAN % Slope limiter (NONE, VENKATAKRISHNAN, VENKATAKRISHNAN_WANG, BARTH_JESPERSEN, VAN_ALBADA_EDGE)
% Monotonic Upwind Scheme for Conservation Laws (TVD) in the adjoint flow equations.
% Required for 2nd order upwind schemes (NO, YES)
VENKAT_LIMITER_COEFF= 0.03
JST_SENSOR_COEFF= ( 0.5, 0.02 ) % 2nd and 4th order artificial dissipation coefficients for the JST method ( 0.5, 0.02 by default )
% Monotonic Upwind Scheme for Conservation Laws (TVD) in the turbulence equations.
% Required for 2nd order upwind schemes (NO, YES)
MUSCL_TURB= YES
% Slope limiter (NONE, VENKATAKRISHNAN, VENKATAKRISHNAN_WANG,
% BARTH_JESPERSEN, VAN_ALBADA_EDGE)
SLOPE_LIMITER_TURB= VENKATAKRISHNAN

% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
% Linear solver or smoother for implicit formulations (BCGSTAB, FGMRES, SMOOTHER_JACOBI,
% SMOOTHER_ILU, SMOOTHER_LUSGS,
% SMOOTHER_LINELET)
LINEAR_SOLVER= FGMRES
LINEAR_SOLVER_PREC= ILU % Preconditioner of the Krylov linear solver (ILU, LU_SGS, LINELET, JACOBI)
LINEAR_SOLVER_ERROR= 1E-6 % Minimum error of the linear solver for implicit formulations
LINEAR_SOLVER_ITER= 5 % Max number of iterations of the linear solver for the implicit formulation
LINEAR_SOLVER_ILU_FILL_IN= 0 % Linear solver ILU preconditioner fill-in level (0 by default)

% -------------------------- MULTIGRID PARAMETERS -----------------------------%
MGLEVEL= 0 % Multi-grid levels (0 = no multi-grid)

% -------------------- FLOW NUMERICAL METHOD DEFINITION -----------------------%
CONV_NUM_METHOD_FLOW= JST % Convective numerical method (JST, LAX-FRIEDRICH, CUSP, ROE, AUSM, AUSMPLUSUP, AUSMPLUSUP2, HLLC, TURKEL_PREC, MSW, FDS)
TIME_DISCRE_FLOW= EULER_IMPLICIT % Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT)
ENTROPY_FIX_COEFF= 0.1 % Entropy fix coefficient (0.0 implies no entropy fixing, 1.0 implies scalar artificial dissipation)
RELAXATION_FACTOR_FLOW= 0.5 % Relaxation coefficient

% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
CONV_NUM_METHOD_TURB= SCALAR_UPWIND % Convective numerical method (SCALAR_UPWIND)
TIME_DISCRE_TURB= EULER_IMPLICIT % Time discretization (EULER_IMPLICIT)
CFL_REDUCTION_TURB= 1.0 % Reduction factor of the CFL coefficient in the turbulence problem
RELAXATION_FACTOR_TURB= 0.5 % Relaxation coefficient

[pcg]

The only documentation is the pull request https://github.com/su2code/SU2/pull/790

MACH_NUMBER= 1E-9 this makes me a bit uneasy because some schemes need a reference Mach number, I don't think JST is one of them but...
By the way some of the options you have are not considered for this scheme, you can read about that here: https://su2code.github.io/docs_v7/Convective-Schemes/

Can you attach the grid? Or is it one of the testcases that ship with SU2?