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Old   January 16, 2013, 21:58
Default JST Artificial Dissipation
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Hi,

I was looking through the JST artificial dissipation code implemented in the function CCentJST_Flow::SetResidual() in numerics_convective.cpp.

I have not been able to find references for some of the scaling factors used in the JST artificial dissipation code.

Can you explain the meaning of "StretchingFactor", "sc2" and "sc4"? Alternatively, can you point out the paper that this is from? Do they have something to do with the aspect ratio of the elements?

Code:
Local_Lambda_i = (fabs(ProjVelocity_i)+SoundSpeed_i*Area); 
Local_Lambda_j = (fabs(ProjVelocity_j)+SoundSpeed_j*Area); 
MeanLambda = 0.5*(Local_Lambda_i+Local_Lambda_j); 
 
Phi_i = pow(Lambda_i/(4.0*MeanLambda+EPS), Param_p); 
Phi_j = pow(Lambda_j/(4.0*MeanLambda+EPS), Param_p);     
StretchingFactor = 4.0*Phi_i*Phi_j/(Phi_i+Phi_j+EPS); 
 
sc2 = 3.0*(double(Neighbor_i)+double(Neighbor_j))/(double(Neighbor_i)*double(Neighbor_j)); 
sc4 = sc2*sc2/4.0; 
Epsilon_2 = Param_Kappa_2*0.5*(Sensor_i+Sensor_j)*sc2; 
Epsilon_4 = max(0.0, Param_Kappa_4-Epsilon_2)*sc4;
/*--- Compute viscous part of the residual ---*/ 
for (iVar = 0; iVar < nVar; iVar++) 
    val_resvisc[iVar] = (Epsilon_2*Diff_U[iVar] - Epsilon_4*Diff_Lapl[iVar])*StretchingFactor*MeanLambda;
Additionally for the papers I have read, the calculation of "Epsilon_2" is,
Code:
Epsilon_2 = Param_Kappa_2*max(Sensor_i, Sensor_j);
Whereas, in the SU2 code, it is the average of the sensor values. Is this done in order to reduce the sensitivity of the sensors?


Thanks,
KW
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Old   January 17, 2013, 04:29
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I would also like to know more about this scheme.

This may be a basic question since I am not very familiar with JST scheme. The JST scheme in SU2 also has first order dissipation, e.g., the config files have

Code:
% 1st, 2nd and 4th order artificial dissipation coefficients
AD_COEFF_FLOW= ( 0.15, 0.5, 0.02 )
What does first order dissipation mean in this context ? The AIAA paper does not clarify how these three coefficients appear in the scheme, I can only see the second and fourth order dissipation explained in the paper.
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Old   January 18, 2013, 22:32
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Quote:
Originally Posted by praveen View Post
I would also like to know more about this scheme.

This may be a basic question since I am not very familiar with JST scheme. The JST scheme in SU2 also has first order dissipation, e.g., the config files have

Code:
% 1st, 2nd and 4th order artificial dissipation coefficients
AD_COEFF_FLOW= ( 0.15, 0.5, 0.02 )
What does first order dissipation mean in this context ? The AIAA paper does not clarify how these three coefficients appear in the scheme, I can only see the second and fourth order dissipation explained in the paper.
The first number (0.15) is the coefficient that SU2 uses in the multigrid levels, where only a first order spatial discretization (Lax–Friedrichs) is used.

Cheers,
Francisco
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Old   January 18, 2013, 22:44
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Quote:
Originally Posted by amphy404 View Post
Hi,

I was looking through the JST artificial dissipation code implemented in the function CCentJST_Flow::SetResidual() in numerics_convective.cpp.

I have not been able to find references for some of the scaling factors used in the JST artificial dissipation code.

Can you explain the meaning of "StretchingFactor", "sc2" and "sc4"? Alternatively, can you point out the paper that this is from? Do they have something to do with the aspect ratio of the elements?

Code:
Local_Lambda_i = (fabs(ProjVelocity_i)+SoundSpeed_i*Area); 
Local_Lambda_j = (fabs(ProjVelocity_j)+SoundSpeed_j*Area); 
MeanLambda = 0.5*(Local_Lambda_i+Local_Lambda_j); 
 
Phi_i = pow(Lambda_i/(4.0*MeanLambda+EPS), Param_p); 
Phi_j = pow(Lambda_j/(4.0*MeanLambda+EPS), Param_p);     
StretchingFactor = 4.0*Phi_i*Phi_j/(Phi_i+Phi_j+EPS); 
 
sc2 = 3.0*(double(Neighbor_i)+double(Neighbor_j))/(double(Neighbor_i)*double(Neighbor_j)); 
sc4 = sc2*sc2/4.0; 
Epsilon_2 = Param_Kappa_2*0.5*(Sensor_i+Sensor_j)*sc2; 
Epsilon_4 = max(0.0, Param_Kappa_4-Epsilon_2)*sc4;
/*--- Compute viscous part of the residual ---*/ 
for (iVar = 0; iVar < nVar; iVar++) 
    val_resvisc[iVar] = (Epsilon_2*Diff_U[iVar] - Epsilon_4*Diff_Lapl[iVar])*StretchingFactor*MeanLambda;
Additionally for the papers I have read, the calculation of "Epsilon_2" is,
Code:
Epsilon_2 = Param_Kappa_2*max(Sensor_i, Sensor_j);
Whereas, in the SU2 code, it is the average of the sensor values. Is this done in order to reduce the sensitivity of the sensors?


Thanks,
KW
As you know, there is not a direct translation from the classical JST method in structured grids to the unstructured world, and probably each unstructured code has a slightly different implementation based on Jameson, Martinelli and Mavriplis works.

Cheers,
Francisco
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