Truncation error in SPH

More documents

Recommendations

Info

Results – uniform particle spacing, 1D sinusoidal test function A(x), wavelength λ 10th order polynomial kernel, β=4 non-dimensionalised L 2 norm error First SPHERIC Workshop, Rome, 2006 10 2 10 0 10 -2 10 -4 10 -6 10 -4 Δx/h= 4/3 0.9 4/7 0.5 0.3 4/19 4/21 0.1 10 -3 analysis, Δx/h=4/(2n+1) computation, Δx/h=4/(2n+1) computation, Δx/h≠4/(2n+1) 10 -2 h/λ (a) 10 -1 1 2 10 0
Non-uniform particle distribution x b is the location of particle b xb A(x) is the centroid of a region associated with particle b xb x b First SPHERIC Workshop, Rome, 2006 Δx b x x − x δ b = Δx b b b
Page 1 and 2: Truncation error in SPH Nathan Quin
Page 3 and 4: Methods Analysis Taylor series expa
Page 5 and 6: The dimensionless kernel Wˆ ( s) =
Page 7 and 8: Discretisation error - uniform part
Page 9 and 10: Overall error - uniform particle sp
Page 11: Results - uniform particle spacing,
Page 15 and 16: Non-uniform spacing - results Norma
Page 17 and 18: First-order consistent kernel (CSPH
Page 19 and 20: 3D SPH Normally distributed random
Page 21 and 22: 3D standard and corrected SPH σ/Δ
Page 27 and 28: 3D standard SPH σ/Δx = 0.02 (low
Page 29 and 30: Conclusions Error depends on • h

Truncation error in SPH

Create successful ePaper yourself

Delete template?

Save as template?