Main.m

clear -all
clc
close all
format long
warning off

Length_domain     = 2*pi   % Total length of the spatial domain (put 1 or 2 for the sinus wave as initial condition)
Viscosity         = 0.0035 % Kinematic viscosity
Number_elements   = 32     % Number of elements (for FE) / nodes (for FD)
Subgrid_constant  = 0.1   % Subgrid terms are implemented for some discretizations
Filter            = -1     % Dynamic Smagorinsky model: type of filter
                                   % <0  = no subgrid model -> DNS
                                   % 0   = deactivated -> use the constant Subgrid_constant)
                                   % 1   = 3-nodes binomial filter
                                   % 2   = 5-nodes binomial filter
                                   % 3   = 7-nodes binomial filter
                                   % 4   = 9-nodes binomial filter
                                   % 5   = Pade filter
Alpha_Pade        = 0.2    % Parameter for the Pade filter, controls the dissipation ]-0.5,0.5[
Order_Viscous     = 6       % = 2, 4, 6 : Order of the discretization for second derivative (used in Hc4 and in nonlinear schemes)
Time_total        = 210     % Time of the simulation (1 for the sinus wave)
Time_steps        = 20000  % Number of time steps, increment in time is thus equal to Time_total/Time_steps
Ninterpolation    = 20;    % The high-order finite elements show oscillations within the elements,
                           % This parameter indicates how many additionnal points are interpolated for each element
Name_output       = 'DGFE_HermiteH3_3.5e-3_32_C0.0' % Name of the output file
Name_spectrum_ref = 'Results/spectrum_2048_35e-4_new.txt'; % Name of the reference turbulence spectrum calculated by a pseudo-spectral method
% Results/spectrum_2048_35e-4_new.txt has 1024 modes and has been calculated for a kinematic viscosity = 0.0035
% Results/spectrum_2048_75e-4_new.txt has 1024 modes and has been calculated for a kinematic viscosity = 0.0075

% Method = 1  : finite element (FE) linear Lagrange P1
% Method = 2  : finite element (FE) cubic Lagrange P3
% Method = 3  : finite element (FE) cubic Hermite H3
% Method = 4  : finite element (FE) 5th order Hermite H5
% Method = 5  : discontinuous Galerkin finite element (DGFE) linear Lagrange P1
% Method = 6  : discontinuous Galerkin finite element (DGFE) cubic Hermite H3
% Method = 7  : finite difference (FD) energy conservative order 2 for convective term
% Method = 8  : finite difference (FD) energy conservative order 4 for convective term
% Method = 9  : finite difference (FD) energy dissipative order 2 for convective term
% Method = 10 : finite difference (FD) compact spectral-like resolution
% Method = 11 : finite difference (FD) non-linear discretization of the convective term
method    = 6 ;
submethod = 1 ; % Used by the nonlinear FD schemes and cubic Lagrange + Hermite FE
M_DGFE    = 20. ; % Used by the discontinuous FE methods, slope limiter minmod 2 (upper bound on second derivative).

addpath('./src/');

switch method
  case 1
     FE_LagrangeP1(Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref);

  case 2
     FE_LagrangeP3(Number_elements,Viscosity,Subgrid_constant,Filter,Length_domain,Time_total,Time_steps,Ninterpolation,Name_output,Name_spectrum_ref,submethod);

  case 3
     FE_HermiteH3 (Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Ninterpolation,Name_output,Name_spectrum_ref,submethod);

  case 4
     FE_HermiteH5 (Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Ninterpolation,Name_output,Name_spectrum_ref,submethod);

  case 5
     DGFE_LagrangeP1(Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,M_DGFE,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref);

  case 6
     DGFE_HermiteH3(Number_elements,Viscosity,M_DGFE,Length_domain,Time_total,Time_steps,Ninterpolation,Name_output,Name_spectrum_ref);

  case 7
     FD_conservative_order2(Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref);

  case 8
     FD_conservative_order4(Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref,Order_Viscous);

  case 9
     FD_dissipative_order2(Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref);

  case 10
     FD_compact_spectral (Number_elements,Viscosity,Subgrid_constant,Filter,Alpha_Pade,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref,submethod) ;

  case 11
     FD_nonlinear_schemes(Number_elements,Viscosity,Subgrid_constant,Length_domain,Time_total,Time_steps,Name_output,Name_spectrum_ref,submethod,Order_Viscous) ;

  otherwise
     disp('The requested method is not implemented yet')

end