2.10 Table of derivative expressions available in Fastflo

In the table below, A represents a general expression, which can involve any known variables, and must be written in braces. As indicated by the suffices and typefaces, A can be a scalar (lower-case typeface), a vector (bold lower-case typeface), or a tensor (bold upper-case typeface). If its value is 1, A can be omitted. U1 can be any unknown, or also any expression written in braces. The summation convention applies to repeated suffices.

Number	Notation	Interpretation
1	`D_jAD_jU1`	$\nabla\cdot(a\nabla u)$
2	`AU1`
3	`A_jD_jU1`	$\mbox{\boldmath{$a$}}\cdot\nabla u$
4	`D_jA_jU1`	$\nabla\cdot(\mbox{\boldmath{$a$}}u)$
5	`D_jA_jkD_kU1`	$\nabla\cdot(A\nabla u)$
6	`D_jAU1_j`	$\mbox{div}(a\mbox{\boldmath{$u$}})$
7	`AD_jU1_j`	$a\mbox{ div }\mbox{\boldmath{$u$}}$
8	`A_jU1_j`	$\mbox{\boldmath{$a$}}\cdot\mbox{\boldmath{$u$}}$
9	`D_jA_kD_kU1_j`	$\mbox{div}(\mbox{\boldmath{$a$}}\cdot\nabla u)$
10	`D_jA_jD_kU1_k`	$\mbox{div}(\mbox{\boldmath{$a$}} \mbox{ div }\mbox{\boldmath{$u$}})$
11	`D_jA_jkU1_k`	$\mbox{div}(A\mbox{\boldmath{$u$}})$
12	`A_jkD_jU1_k`	$\mbox{div }A\mbox{\boldmath{$u$}}$
13	`D_iAU1`	$\nabla(au)$
14	`AD_iU1`	$a\nabla u$
15	`A_iU1`	$\mbox{\boldmath{$a$}}u$
16	`D_iA_jD_jU1`	$\nabla(\mbox{\boldmath{$a$}}\cdot\nabla u)$
17	`D_jA_jD_iU1`	$\nabla\cdot(\mbox{\boldmath{$a$}}\nabla u)$
18	`D_jA_jiU1`	$\nabla\cdot(Au)$
19	`A_ijD_jU1`	$A\nabla u$
20	`AU1_i`	$a\mbox{\boldmath{$u$}}$
21	`A_jD_jU1_i`	$\mbox{\boldmath{$a$}}\cdot\nabla\mbox{\boldmath{$u$}}$
22	`D_jA_jU1_i`	$\mbox{\boldmath{$a$}}\cdot\nabla\mbox{\boldmath{$u$}}+\mbox{\boldmath{$u$}}\mbox{ div }\mbox{\boldmath{$a$}}$
23	`D_jAD_jU1_i`	$\nabla\cdot(a\nabla\mbox{\boldmath{$u$}})$
24	`D_jA_jkD_kU1_i`	$\nabla\cdot(A\nabla\mbox{\boldmath{$u$}})$
25	`D_iAD_jU1_j`	$\nabla(a\nabla\cdot\mbox{\boldmath{$u$}})$
26	`D_iA_jU1_j`	$\nabla(\mbox{\boldmath{$a$}}\cdot\mbox{\boldmath{$u$}})$
27	`D_jAD_iU1_j`	$\nabla(a\nabla\cdot\mbox{\boldmath{$u$}})-\nabla a\nabla\cdot\mbox{\boldmath{$u$}}$
28	`A_jD_iU1_j`	$\mbox{\boldmath{$a$}}\cdot(\nabla\mbox{\boldmath{$u$}})$
29	`D_jA_iU_j`	$\mbox{\boldmath{$a$}}(\nabla\cdot\mbox{\boldmath{$u$}})-\mbox{\boldmath{$u$}}\cdot\nabla\mbox{\boldmath{$a$}}$
30	`A_iD_jU1_j`	$\mbox{\boldmath{$a$}}(\nabla\cdot\mbox{\boldmath{$u$}})$
31	`A_ijU1_j`	$A\mbox{\boldmath{$u$}}$
32	`D_iA_jkD_jU1_k`	$\nabla(A\cdot\nabla\mbox{\boldmath{$u$}})$
33	`D_jA_jkD_iU1_k`
34	`D_jA_ikD_kU1_j`
35	`D_jA_ijD_kU1_k`
36	`D_jA_ikD_jU1_k`
37	`D_jA_kD_jU1_k`	$\mbox{div }\mbox{\boldmath{$a$}}\nabla\mbox{\boldmath{$u$}}$
38	`D_jA_iD_jU1`	$\mbox{div }\mbox{\boldmath{$a$}}\nabla u$