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doc:user:integration:scheme:dynexpl

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doc:user:integration:scheme:dynexpl [2014/10/07 17:58] jorisdoc:user:integration:scheme:dynexpl [2016/03/30 15:23] – external edit 127.0.0.1
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 This scheme is conditionally stable (time step limited) and non dissipative. This scheme is conditionally stable (time step limited) and non dissipative.
  
-==== alpha-generalized scheme ====+==== Alpha-generalized scheme ====
  
 Same relations as in the implicit [[dynimpl|alpha-generalized]] scheme, but with the parameter used to weight internal and external forces equal to 1, leading to : Same relations as in the implicit [[dynimpl|alpha-generalized]] scheme, but with the parameter used to weight internal and external forces equal to 1, leading to :
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 Conditionally stable. Conditionally stable.
  
-==== Le schema Tchamwa ====+==== Tchamwa Scheme ==== 
 + 
  
 Explicit algorithm where numerical dissipation is monitored by the parameter $\phi$.  Explicit algorithm where numerical dissipation is monitored by the parameter $\phi$. 
  
-Equilibrium calculated with+Equilibrium computed with
  
 $$a(t^{n+1}) = \frac{F^{ext}(t^{n+1}) - F^{int}(t^{n+1})}{M}$$ $$a(t^{n+1}) = \frac{F^{ext}(t^{n+1}) - F^{int}(t^{n+1})}{M}$$
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 Relation between $\phi$ and spectral radius for the bifurcation $\rho_\beta$ (user parameter ''MDR_ECHR'') is: Relation between $\phi$ and spectral radius for the bifurcation $\rho_\beta$ (user parameter ''MDR_ECHR'') is:
   * $$\phi = \frac{2(1- \rho_\beta^{1/2})}{(1-\rho_\beta)} \mbox{ if } \rho_\beta < 1 $$   * $$\phi = \frac{2(1- \rho_\beta^{1/2})}{(1-\rho_\beta)} \mbox{ if } \rho_\beta < 1 $$
-  * $$\phi = 1 \mbox{ if} \rho_\beta = 1 $$+  * $$\phi = 1 \mbox{ if } \rho_\beta = 1 $$
  
-===== Data set =====+===== Input file =====
  
 See [[dynimpl|dynamic implicit]] scheme for definition of density and initial velocities. See [[dynimpl|dynamic implicit]] scheme for definition of density and initial velocities.
  
-==== Choosing the algorithm ====+==== Old Metafor Version <= 2422 ====
  
-^       Scheme       ^  ''MDE_NDYN''  ^  ''MDR_ECHR'' +=== Choosing the algorithm === 
-Chung Hulbert       |                    X      + 
-Différence centrée  |                           +^       Scheme         ^  ''MDE_NDYN''  ^  ''MDR_ECHR'' 
-| Tchamwa             |              |            |+Certered difference  |                             
 +Chung Hulbert        |                    X        
 +| Tchamwa              |              |              |
  
 (see [[doc:user:integration:general:parameters]]) (see [[doc:user:integration:general:parameters]])
 +
 +==== New Metafor Version > 2422 ====
 +
 +=== Centered Difference ===
 +
 +<code>
 +ti = CentralDifferenceTimeIntegration(metafor)
 +metafor.setTimeIntegration(ti)
 +</code>
 +
 +=== Chung Hulbert ===
 +
 +<code>
 +ti = ChExplicitTimeIntegration(metafor)
 +ti.setRhoB(_rhoB)
 +metafor.setTimeIntegration(ti)
 +</code>
 +
 +The parameter ''_rhoB'' is the spectral radius at bifurcation point ([0, 1]). The default value is 0.8182.
 +
 +=== Tchamwa === 
 +
 +<code>
 +ti = TchamwaTimeIntegration(metafor)
 +ti.setRhoB(_rhoB)
 +metafor.setTimeIntegration(ti)
 +</code>
 +
 +The parameter ''_rhoB'' is the spectral radius at bifurcation point ([0, 1]). The default value is 0.8182.
  
 Other parameters : see [[quasistatique]] Other parameters : see [[quasistatique]]
doc/user/integration/scheme/dynexpl.txt · Last modified: 2022/12/21 11:35 by boman

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