Truncation error in SPH
Truncation error in SPH
Truncation error in SPH
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Kernel boundary smoothness<br />
Boundary smoothness of the kernel<br />
is the highest <strong>in</strong>teger β for which<br />
the β th derivative and all lower<br />
derivatives are zero at the<br />
boundaries of the compact support.<br />
cubic B-spl<strong>in</strong>e kernel: β=2<br />
Gaussian kernel: β→∞ <strong>in</strong> <strong>in</strong>f<strong>in</strong>ite doma<strong>in</strong><br />
polynomial kernel: arbitrary β<br />
First <strong>SPH</strong>ERIC Workshop, Rome, 2006<br />
ˆ<br />
W<br />
ˆ<br />
W ′<br />
ˆ<br />
W ′′<br />
ˆ<br />
W ′′′<br />
1<br />
0.5<br />
0<br />
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2<br />
1<br />
0<br />
-1<br />
-2<br />
2<br />
-1.5 -1 -0.5 0 0.5 1 1.5 2<br />
0<br />
-2<br />
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2<br />
5<br />
0<br />
-5<br />
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2<br />
s = ( (x-x x − )/h<br />
i x ) h<br />
a
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