Elimination of Bad Volume

A finite volume is considered bad, if:
  • The volume is negative, or less than a minimum volume
  • The mass or the energy of the volume is negative

For both cases, the bad volume is merged with its neighbors. This merge is iterative as the neighbors could also be a bad volume.

To determine the minimum volume, two approaches are used:
  1. The mean volume, V ¯ of all the active volume is calculated and a first minimum volume is a fraction of this one:
    (1)
    V min 1 = V ¯ C g m e r g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwbWaaS baaSqaaiGac2gacaGGPbGaaiOBaiaaigdaaeqaaOGaeyypa0JabmOv ayaaraGaeyyXICTaam4qamaaBaaaleaacaWGNbGaamyBaiaadwgaca WGYbGaam4zaaqabaaaaa@45E8@

    Where, C g m e r g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGNbGaamyBaiaadwgacaWGYbGaam4zaaqabaaaaa@3B95@ is the "Factor for global merging" user-defined in /MONVOL/FVMBAG1.

    The flag I g m e r g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaadEgacaWGTbGaamyzaiaadkhacaWGNbaabeaaaaa@3D0D@ determines if the mean volume to use is the current mean volume ( I g m e r g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaadEgacaWGTbGaamyzaiaadkhacaWGNbaabeaaaaa@3D0D@ =1) or the initial mean volume calculated at the first cycle.

  2. The mean volume, V ¯ n of all the neighbors of the current one is calculated. A second minimum volume is a fraction of the previous one: (2)
    V min 2 = V ¯ n C n m e r g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwbWaaS baaSqaaiGac2gacaGGPbGaaiOBaiaaikdaaeqaaOGaeyypa0JabmOv ayaaraWaaSbaaSqaaiaad6gaaeqaaOGaeyyXICTaam4qamaaBaaale aacaWGUbGaamyBaiaadwgacaWGYbGaam4zaaqabaaaaa@4719@

    Where, C n m e r g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGNbGaamyBaiaadwgacaWGYbGaam4zaaqabaaaaa@3B95@ is the "Factor for neighborhood merging" user-defined in /MONVOL/FVMBAG1.

    Finally, the volume minimum used is: (3)
    V min = min ( V min 1 , V min 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGwbWaaS baaSqaaiGac2gacaGGPbGaaiOBaaqabaGccqGH9aqpciGGTbGaaiyA aiaac6gadaqadaqaaiaadAfadaWgaaWcbaGaciyBaiaacMgacaGGUb GaaGymaaqabaGccaGGSaGaamOvamaaBaaaleaaciGGTbGaaiyAaiaa c6gacaaIYaaabeaaaOGaayjkaiaawMcaaaaa@4A99@