SPH

Question 1

3 axioms

Answer 1

• partition of unity
• weighting or kernel function, tends to the delta function as the smoothing length tends to zero
• kernel is K times differentiable and is continuous

Question 2

Partition of unity

Answer 2

• comes from the Dirac Delta function which possesses 2 important properties for integration of a function f(x)
• if partition of unity is not satisfied, then the support of the smoothing kernel is not complete
• this means there are an insufficient number of particles within the summation to ensure an accurate result

Question 3

SPH with free surface

Answer 3

• partition of unity should be 1, low order kernel and low number of particles reduce accuracy
• a free surface truncates the support so the answer is less than it should be
• this results in poor quality approximations for the movement of the free surface with errors appearing in predicting the correct movement of the surface

Question 4

Weakly compressible flow

Answer 4

• models incompressible fluids by solving both the continuity equation and momentum equations
• such that compressibility effects are restricted to less than 1%
• this is enforced by choosing the speed of sound, Co, such that mach number M = Vmax/Co is 0.1 or less

Question 5

SPH written in lagrangian

Answer 5

• meshless method with moving particles

- governing equations are written in lagrangian not eularian