Stability of Two Dimensional Immiscible Flow to Viscous Fingering
Stability of Two Dimensional Immiscible Flow to Viscous Fingering
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In our eReader you can find the full English version of the book. Read Stability of Two Dimensional Immiscible Flow to Viscous Fingering Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Stability of Two Dimensional Immiscible Flow to Viscous Fingering
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With J, j and n denoting respectively the x, y and t indices, the numerical scheme used for (4a) consists of advection terms discretized by a leap-frog stencil, the viscosity term by a Crank-Nicholson stencil: 2 Af Ax A:y = — ^ — Ip" a iu"*^ ■¥ uV^) + J?" A (u""^^ -t- u"~^n 4 Ax^ 1 ' •■' ' ' ••' ' •■/ '''i "^'^"rj "r, ]>j - — I?" A (u"^^ + i/""^) -^ b" a (m""^^ -t- m''~^)1, 4Ay^ (8) where 8, * J ■ 8 81- J - 8 2 "f. Y ^ "I- 1, J A, u'l^j - uf^^j - ulj, Equation (4b) has the form V • X(5) VP = V ...his) V5, and was approximated by a Crank-Nicholson stencil: (9) (10) -7- The difference scheme is second order accurate in space and time. The linear system of equations generated on the numerical grid for each equation at each timestep were inverted using a multigrid algorithm^ of relaxation and injection through a sequence of coarser grids which is based on a variational formulation of the equations (4). The calculations were performed in a square, length L, width L. The boundary condi- tions imposed were (5 is defined in (11)) 5=1, at^^O, 5 = 0, aXy = L, — = at X = 0, Z, , dx P = Po, at >- = 0, P = 0, aty = L, (11) — = &tx = 0, L, dx uix, y, f = 0) = UQix, y) .
What to read after Stability of Two Dimensional Immiscible Flow to Viscous Fingering?
You can find similar books in the "Read Also" column, or choose other free books by Michael J King to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
With J, j and n denoting respectively the x, y and t indices, the numerical scheme used for (4a) consists of advection terms discretized by a leap-frog stencil, the viscosity term by a Crank-Nicholson stencil: 2 Af Ax A:y = — ^ — Ip" a iu"*^ ■¥ uV^) + J?" A (u""^^ -t- u"~^n 4 Ax^ 1 ' •■' ' ' ••' ' •■/ '''i "^'^"rj "r, ]>j - — I?" A (u"^^ + i/""^) -^ b" a (m""^^ -t- m''~^)1, 4Ay^ (8) where 8, * J ■ 8 81- J - 8 2 "f. Y ^ "I- 1, J A, u'l^j - uf^^j - ulj, Equation (4b) has the form V • X(5) VP = V ...his) V5, and was approximated by a Crank-Nicholson stencil: (9) (10) -7- The difference scheme is second order accurate in space and time. The linear system of equations generated on the numerical grid for each equation at each timestep were inverted using a multigrid algorithm^ of relaxation and injection through a sequence of coarser grids which is based on a variational formulation of the equations (4). The calculations were performed in a square, length L, width L. The boundary condi- tions imposed were (5 is defined in (11)) 5=1, at^^O, 5 = 0, aXy = L, — = at X = 0, Z, , dx P = Po, at >- = 0, P = 0, aty = L, (11) — = &tx = 0, L, dx uix, y, f = 0) = UQix, y) .
What to read after Stability of Two Dimensional Immiscible Flow to Viscous Fingering?
You can find similar books in the "Read Also" column, or choose other free books by Michael J King to read onlineMoreLess
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