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By Lieut. Col W. E. Wilson-Johnston

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Additional resources for An Account of the Operations of the 18th (Indian) Division in Mesopotamia. December, 1917, to December, 1918

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10) can be written as N � fi (x)� = j=1 mj fj (x ′ ) W (x − x ′ , h), ρj N �∇fi (x)� = − j=1 mj fj (x ′ )∇W (x − x ′ , h). 14) ∂W (x − x ′ , h) mj fj (x ′ ) . ρj ∂xi Here, we use ρ(x) instead of f(x). 11), ρ(x) can be obtained as N �ρi (x)� = j=1 mj W (x − x ′ , h). 15) This states that the density of particles can be approximated by the weighted average of particle densities within the influence domain of a particle. 1 Governing Equations Navier–Stokes (N–S) equations are introduced in this section as the governing equations to describe the incompressible Newtonian fluid.

Suleman, A. (2012). A robust weakly compressible SPH method and its comparison with an incompressible SPH. International Journal for Numerical Methods in Engineering, 89(8), 939–956. , & Jin, Y. C. (2011). A mesh-free particle model for simulation of mobile-bed dam break. Advances in Water Resources, 34(6), 794–807. Shao, S. D. (2010). Incompressible SPH flow model for wave interactions with porous media. Coastal Engineering, 57, 304–316. Shao, S. , Ji, C. , Graham, D. , Reeve, D. , James, P.

1998). Newtonian hydrodynamics of the coalescence of black holes with neutron stars ii, tidally locked binaries with a soft equation of state. Monthly Notices of the Royal Astronomical Society, 308, 780–794. Lee, W. H. (2000). Newtonian hydrodynamics of the coalescence of black holes with neutron stars iii, irrotational binaries with a stiff equation of state. Monthly Notices of the Royal Astronomical Society, 318, 606–624. Liu, M. , Liu, G. , & Lam, K. Y. (2003). A one-dimensional meshfree particle formulation for simulating shock waves.

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