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For both Anelastic and Fully Compressible
-Positivity-Preserving Energy-Conserving Semi-Implicit, if this is possible
-Multiderivative Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Relaxation Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Invariant-Domain Preserving Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Adaptive Time Stepping (fully compressible will need the IMEX/HEVI version of this), especially relaxation, SSP and invariant-domain preserving versions
For Fully Compressible
-HEVI- KG, SSP and "energy-conserving" variants
Basically, what we are searching for here is a scheme with large explicit time step (both the ability to handle sound waves in the fully compressible case and a large imaginary stability region) that preserves total energy and also positivity. Our existing schemes typically get just one or two of these properties:
-semi-implicit allows a long time step and preserves energy but not positivity
-KGRK (and IMEX/HEVI variants) allows a long time step but doesn't preserve energy or positivity
-SPP (and IMEX/HEVI variants) preserves positivity but doesn't allow a long time or preserve energy
Of the three properties, we can probably give up exact energy conservation the easiest
The text was updated successfully, but these errors were encountered:
For both Anelastic and Fully Compressible
-Positivity-Preserving Energy-Conserving Semi-Implicit, if this is possible
-Multiderivative Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Relaxation Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Invariant-Domain Preserving Runge-Kutta (fully compressible will need the IMEX/HEVI version of this)
-Adaptive Time Stepping (fully compressible will need the IMEX/HEVI version of this), especially relaxation, SSP and invariant-domain preserving versions
For Fully Compressible
-HEVI- KG, SSP and "energy-conserving" variants
Basically, what we are searching for here is a scheme with large explicit time step (both the ability to handle sound waves in the fully compressible case and a large imaginary stability region) that preserves total energy and also positivity. Our existing schemes typically get just one or two of these properties:
-semi-implicit allows a long time step and preserves energy but not positivity
-KGRK (and IMEX/HEVI variants) allows a long time step but doesn't preserve energy or positivity
-SPP (and IMEX/HEVI variants) preserves positivity but doesn't allow a long time or preserve energy
Of the three properties, we can probably give up exact energy conservation the easiest
The text was updated successfully, but these errors were encountered: