<s>
In	O
numerical	B-Algorithm
methods	I-Algorithm
,	O
total	B-Algorithm
variation	I-Algorithm
diminishing	I-Algorithm
(	O
TVD	O
)	O
is	O
a	O
property	O
of	O
certain	O
discretization	B-Algorithm
schemes	O
used	O
to	O
solve	O
hyperbolic	O
partial	O
differential	O
equations	O
.	O
</s>
<s>
A	O
numerical	B-Algorithm
method	I-Algorithm
is	O
said	O
to	O
be	O
total	B-Algorithm
variation	I-Algorithm
diminishing	I-Algorithm
(	O
TVD	O
)	O
if	O
,	O
</s>
<s>
A	O
TVD	B-Algorithm
scheme	I-Algorithm
is	O
monotonicity	O
preserving	O
.	O
</s>
<s>
In	O
Computational	O
Fluid	O
Dynamics	O
,	O
TVD	B-Algorithm
scheme	I-Algorithm
is	O
employed	O
to	O
capture	O
sharper	O
shock	O
predictions	O
without	O
any	O
misleading	O
oscillations	O
when	O
variation	O
of	O
field	O
variable	O
“”	O
is	O
discontinuous	O
.	O
</s>
<s>
The	O
use	O
of	O
coarse	O
grids	O
with	O
central	B-Algorithm
difference	I-Algorithm
scheme	I-Algorithm
,	O
upwind	B-Algorithm
scheme	I-Algorithm
,	O
hybrid	O
difference	O
scheme	O
,	O
and	O
power	O
law	O
scheme	O
gives	O
false	O
shock	O
predictions	O
.	O
</s>
<s>
TVD	B-Algorithm
scheme	I-Algorithm
enables	O
sharper	O
shock	O
predictions	O
on	O
coarse	O
grids	O
saving	O
computation	O
time	O
and	O
as	O
the	O
scheme	O
preserves	O
monotonicity	O
there	O
are	O
no	O
spurious	O
oscillations	O
in	O
the	O
solution	O
.	O
</s>
<s>
Total	B-Algorithm
variation	I-Algorithm
diminishing	I-Algorithm
scheme	O
makes	O
an	O
assumption	O
for	O
the	O
values	O
of	O
and	O
to	O
be	O
substituted	O
in	O
the	O
discretized	B-Algorithm
equation	O
as	O
follows	O
:	O
</s>
<s>
To	O
overcome	O
these	O
drawbacks	O
,	O
various	O
high-resolution	B-Algorithm
,	O
non-linear	O
techniques	O
have	O
been	O
developed	O
,	O
often	O
using	O
flux/slope	O
limiters	O
.	O
</s>
