FLUX#

FLUX = {flux_type} <bc_id> <blk_id> <species_id> <file_name> [profile]


Description / Usage#

FLUX cards are used to calculate the integrated fluxes of momentum, mass, energy, etc. on a specified side set during post processing. As many of these FLUX cards as desired can be input to Goma to direct the calculations. For example, multiple cards may be used to compute a particular flux, e.g. FORCE_NORMAL, on different side sets or different fluxes on the same side set. Cards with identical fluxes and identical side sets could be used to output the flux calculations to different files. Definitions of the input parameters are:

 {flux_type} A keyword that can have any one of the following values: FORCE_NORMAL FORCE_TANGENT1 FORCE_TANGENT2 FORCE_X FORCE_Y FORCE_Z VOLUME_FLUX SPECIES_FLUX HEAT_FLUX TORQUE AVERAGE_CONC SURF_DISSIP AREA VOL_REVOLUTION PORE_LIQ_FLUX CHARGED_SPECIES_FLUX CURRENT_FICKIAN CURRENT ELEC_FORCE_NORMAL ELEC_FORCE_TANGENT1 ELEC_FORCE_TANGENT2 ELEC_FORCE_X ELEC_FORCE_Y ELEC_FORCE_Z NET_SURF_CHARGE ACOUSTIC_FLUX_NORMAL ACOUSTIC_FLUX_TANGENT1 ACOUSTIC_FLUX_TANGENT2 ACOUSTIC_FLUX_X ACOUSTIC_FLUX_Y ACOUSTIC_FLUX_Z For every request, the integral of the diffusive portion followed by that of the convective portion over the requested boundary will be appended to the specified file. If the convective flux is not applicable (i.e.for flux_types VOLUME_FLUX, TORQUE, AVERAGE_CONC and AREA), the second quantity will be zero. In all cases the area of the face (covered by the entire side set) and the time value are also output. The boundary flag identifier, an integer associated with the boundary location (side set in EXODUS II) in the problem domain on which the integrated flux is desired. An integer that designates the mesh block (material) from which the flux integral should be performed. This has implications on internal boundaries. An integer that identifies the species number if an integrated species flux is requested. A character string corresponding to a file name into which these fluxes should be printed. [profile] Inclusion of the optional string “profile’ to this card will cause the coordinates (x,y,z), the diffusive integrand, and the convective integrand at each integration point to be printed to the file designated above. You can, for example, print out a pressure distribution used to compute a force.

Examples#

The following example shows a sample input deck section that requests five such integrated fluxes:

Post Processing Fluxes =

FLUX = FORCE_X 5 1 0 side5.out

FLUX = FORCE_Y 5 1 0 side5prof.out   profile

FLUX = FORCE_NORMAL 8 1 0 side8.out

FLUX = FORCE_TANGENT1 8 1 0 side8.out

FLUX = VOLUME_FLUX 8 1 0 side8.out

END OF FLUX


Technical Discussion#

The permissible flux types are those listed in file mm_post_def.h for struct Post_Processing_Flux_Names, pp_flux_names being one variable of this struct type.

The flux integrations are carried out as follows:

 FLUX DIFFUSIVE FLUX CONVECTIVE FLUX FORCE_NORMAL $$\int$$ n • $$\underline{T}$$ • ndA $$\int\rho$$ n • (v - $$v_m$$) v • ndA FORCE_TANGENT1 $$\int_1$$ • $$\underline{T}$$ • ndA $$\int\rho$$ $$t_1$$ (v - $$v_m$$) v • ndA FORCE_TANGENT2 $$\int_2$$ • $$\underline{T}$$ • ndA $$\int\rho$$ $$t_2$$ (v - $$v_m$$) v • ndA FORCE_X $$\int$$ i • $$\underline{T}$$ • ndA $$\int\rho$$ i (v - $$v_m$$) v • ndA FORCE_Y $$\int$$ j • $$\underline{T}$$ • ndA $$\int\rho$$ j (v - $$v_m$$) v • ndA FORCE_Z $$\int$$ k • $$\underline{T}$$ • ndA $$\int\rho$$ k (v - $$v_m$$) v • ndA VOLUME_FLUX $$\int$$ n • (v - $$v_m$$) dA for ARBITRARY mesh motion. $$\int$$ n • ddA for LAGRANGIAN mesh motion. SPECIES_FLUX $$\int$$ (-$$D_jn$$ • $$\Delta$$ cj) dA $$\int\rho$$ n • ( v - $$v_m$$ ) cjdA HEAT_FLUX $$\int$$ (-kn • $$\Delta$$ T) dA $$\int\rho$$ CpTn • ( v - $$v_m$$ ) dA TORQUE $$\int$$ $$re_r$$ × ( $$\underline{T}$$ • n) dA AVERAGE_CONC $$\int$$ cjdA SURF_DISSIP $$\int\sigma\Delta$$ v • ( $$\zeta$$ - nn) dA AREA $$\int$$ dA VOL_REVOLUTION $$\int\frac{1}{2}$$ $$\frac{r}{\sqrt{}{1 + (dr/dz)^2}}$$ dA POR_LIQ_FLUX $$\int$$ n • ($$\rho_lv_{darcy}$$) dA CHARGED_SPECIES_FLUX $$\int$$ (-Djn • $$\Delta$$ cj) dA $$\int\rho$$ n • ( v - $$v_m$$ ) cjdA CURRENT_FICKIAN $$\int$$ (-Djn • $$\Delta$$ cj) dA $$\int\rho$$ n • ( v - $$v_m$$ ) cjdA PVELOCITY[1-3] $$\int$$ n • pvjdA ELEC_FORCE_NORMAL $$\int$$ n $$\underline{T}_e$$ • ndA ELEC_FORCE_TANGENT1 $$\int$$ $$t_1$$ • $$\underline{T}_e$$ • ndA ELEC_FORCE_TANGENT2 $$\int$$ $$t_2$$ • $$\underline{T}_e$$ • ndA ELEC_FORCE_X $$\int$$ i • $$\underline{T}_e$$ • ndA ELEC_FORCE_Y $$\int$$ j • $$\underline{T}_e$$ • ndA ELEC_FORCE_Y $$\int$$ k • $$\underline{T}_e$$ • ndA NET_SURF_CHARGE $$\int$$ (-$$\varepsilon$$ $$\underline{n}$$ • $$\underline{E}$$) dA ACOUSTIC_FLUX_NORMAL $$\int$$ (-$$\frac{1}{kR}$$ n • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ n • $$\Delta P_{real}$$) dA ACOUSTIC_FLUX_TANGENT1 $$\int$$ (-$$\frac{1}{kR}$$ $$t_1$$ • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ $$t_1$$ • $$\Delta P_{real}$$) dA ACOUSTIC_FLUX_TANGENT2 $$\int$$ (-$$\frac{1}{kR}$$ $$t_2$$ • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ $$t_2$$ • $$\Delta P_{real}$$) dA ACOUSTIC_FLUX_X $$\int$$ (-$$\frac{1}{kR}$$ $$i$$ • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ $$i$$ • $$\Delta P_{real}$$) dA ACOUSTIC_FLUX_Y $$\int$$ (-$$\frac{1}{kR}$$ $$j$$ • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ $$j$$ • $$\Delta P_{real}$$) dA ACOUSTIC_FLUX_Z $$\int$$ (-$$\frac{1}{kR}$$ $$k$$ • $$\Delta P_{imag}$$) dA $$\int$$ (-$$\frac{1}{kR}$$ $$k$$ • $$\Delta P_{real}$$) dA

The SURF_DISSIP card is used to compute the energy dissipated at a surface by surface tension (Batchelor, 1970). The VOL_REVOLUTION card is used in axi- symmetric problems to compute the volume swept by revolving a surface around the axis of symmetry (z-axis). Even though every flux card results in the area computation of the side set, the AREA card is used when the area of a surface is part of an augmenting condition. The POR_LIQ_FLUX term is valid only for saturated media and the Darcy velocity is defined by $$\nu_{darcy}$$ = ($$\kappa$$ / $$\mu$$) $$\Delta$$ $$p_{liq}$$ . For the more general case, refer to the POROUS_LIQ_FLUX_CONST boundary condition.

References#

Batchelor, JFM, 1970. ….. need to fill-in reference; get from RBS

For information on using flux calculations as part of augmenting conditions, see:

SAND2000-2465: Advanced Capabilities in Goma 3.0 - Augmenting Conditions, Automatic Continuation, and Linear Stability Analysis, I. D. Gates, I. D., Labreche, D. A. and Hopkins, M. M. (January 2001).