Implementing Finite Volume algorithms on GPUs - many-core.group ...

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<strong>Finite</strong> <strong>Volume</strong> Methods <strong>Finite</strong> <strong>Volume</strong> methods store cell-averages of conserved quantities: density, momentum, energy FV methods maintain conservation of these Use rectangular structured grids for efficiency Discretise with cell-centred averages u i,j General update formula: u n+1 i,j = u n ,ji + ∆t(F i−1/2,j − F i+1/2,j ) Need to calculate appropriate fluxes F i+1/2,j for each cell boundary Each flux calculation independent of all others <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 4 / 22
Euler’s equations Flux-conservative form: Euler’s equations ∂u ∂t + ∇ · F(u) = 0 ∂ρ ∂t + ∇ · (ρv) = 0 , ∂ρv ∂t + ∇ · (ρuT u + pI) = 0 , ∂E ∂t + ∇ · ((E + p)v) = 0 <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 5 / 22
Page 1 and 2: Implementing <stro
Page 3 and 4: Applications of Finite</str
Page 5 and 6: Applications of Finite</str
Page 7: Shock-bubble simulation shockBubble
Page 11 and 12: Data layout in memory We use Struct
Page 13 and 14: MUSCL-Hancock scheme Piecewise-cons
Page 15 and 16: MUSCL-Hancock scheme Piecewise-cons
Page 17 and 18: Loading global data into shared mem
Page 19 and 20: Loading global data into shared mem
Page 21 and 22: Within shared memory Thread i − 1
Page 31 and 32: Thread-block layout Each cell depen
Page 33 and 34: Thread-block layout Each cell depen
Page 35 and 36: How fast? We should now check how f
Page 37 and 38: How fast? We should now check how f
Page 39 and 40: Templating over coordinate directio
Page 41 and 42: What block-size should we use? (x-d
Page 43 and 44: Performance on different sized grid
Page 45 and 46: Summary Achieved 147x speed-up for
Page 47: Future investigations Efficient ext

Implementing Finite Volume algorithms on GPUs - many-core.group ...

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