High order well balaced schemes for systems of - Philippe LeFloch

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Forward Euler in timeFirst order schemeHow to do it in such a way that the scheme is conservativeand well balanced?Basic idea: use conservative variable for the evolution,and equilibrium variables to help the reconstruction
Page 1 and 2: High order well balanced schemesfor
Page 3 and 4: Outline• Well balanced schemes•
Page 6 and 7: Some references (not complete!)Bern
Page 9 and 10: When and why does it work?• The m
Page 11: Conservative and equilibrium variab
Page 15 and 16: Well balanced propertyIt is easy to
Page 17 and 18: Time integration: central Runge-Kut
Page 19 and 20: Computation of the stage values 2/2
Page 21 and 22: Unstaggered gridsskipEvolution equa
Page 23 and 24: High order schemesCan be obtained b
Page 25 and 26: Numerical tests• Models considere
Page 27 and 28: Shallow water - static equilibiumN
Page 29 and 30: Shallow water - moving equilibiumN
Page 31 and 32: Accuracy test (smooth solution)Skip
Page 33 and 34: Moving Equilibrium1.2• Initial Co
Page 35 and 36: 4 th order scheme• Left: h, Right
Page 37 and 38: Nozzle flowEuler equations on a cha
Page 39 and 40: Nozzle flow - shock capturing and W
Page 41 and 42: Nozzle flow: accuracy test
Page 43 and 44: summary of ADER schemes• The solu
Page 45 and 46: Numerical reconstruction of(A.Khe,
Page 47 and 48: Numerical local equilibriaSolve Eq.
Page 49 and 50: High order schemesAre obtained by h
Page 51 and 52: RemarkThis property is satisfied by
Page 53 and 54: Application to scalar equationBotto
Page 55 and 56: Fourth order scheme
Page 57: Application to shallow water
Page 60 and 61: Shallow water system4 th Order Sche
Page 62 and 63:
Reconstruction: movingTotal heightD
Page 64:
ConclusionHigh order WB can be obta
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High order well balaced schemes for systems of - Philippe LeFloch

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