Improvements to SOIL: An Eulerian hydrodynamics code Page: 4 of 20
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II. PRESENT SOIL ALGORITHMS
SOIL (Johnson 1971a)1 uses a splitting technique in order to solve the
two-dimensional set of Eulerian hydrodynamic equations. The solution is also
obtained in two phases, a Lagrangian phase followed by a REMAP to the Fillerian
mesh. The Lagrangian phase is fairly standard as in the early one-dimensional
codes FFF2. In the advection phase an extrapolation on velocity is used which
makes the code approach second-order accuracy. Shocks can be treated using a
combination of quadratic and linear pseudo-viscosity terms; the added
viscosity can be used in the expansion phase as well as in compression. The
zoning is strictly rectangular but with variable size zones in the r and z
directions. The code can also be used in x, y geometry. The differential
equations approximated by finite differences forms and solved in (PHI) the
Lagrangian phase and (PH2) the Eulerian Phase (from Ref. 3), are
• ZMi (1)
The equations solved in the Eulerian Phase (PH2) are
|^ + V* (pu) - 0
+ p(u*v)u = 0
The advection, or phase 2(PH2) differencing scheme can be derived from
the following considerations (see Fig. 1).
p _ -VP
— (a^+E) - -PV*u
4 A y_k
K + 1
* ZAX *■
i - 1 i i + 1
Fig. 1. Advection scheme for SOIL.
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Davis, C.G. Improvements to SOIL: An Eulerian hydrodynamics code, report, April 1, 1988; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1064690/m1/4/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.