Hi,
Let us suppose we have three real matrices A, B, C and let \circ denote the Hadamard product, while AB is the conventional matrix product. Is this relation true for all A, B, C matrices:
C \circ (AB) = A( C\circ B)?
I looked at it more thoroughly and I realized that this assumption is...
If I understand well, you want to make the counter smaller than the denominator. It can be done winthin an inline environment as eg.
Let us see the following equation: $\frac{a}{\displaystyle a}$
I would like the determine the work done by gravity on a mass attached to a rod (see the attached image). The rod is assumed to be weightless and rigid.
I start from the definition of work:
W_{AB} = \int_{\mathbf{r}_A}^{\mathbf{r}_B} \mathbf{G}\cdot \mathrm{d}\,\mathbf{r}.
In the x-y coordinate...
So if I am not mistaken I should do the following for each particle:
1. Solve the initial-value problem to gain \vec{r}(t,\vec{R}) at different time steps. For this I must solve an IVP consisting of 2 equations because of the 2D-problem. But I have \vec{v} at discrete points at each time.
2...
Dear all,
I solved the Navier-Stokes equations in Eulerian description. I would like to illustrate it as follows:
I thought to place particles in the domain which will characterize the fluid flow. However I must know the particle position in the Lagrangian specification. As I place the...
I do not know the finite difference approach, but I speak about the steady-state spectral or finite element solution of the problem. To prevent the checkerboard pressure distribution, one should use elements that satisfies the Babuska-Brezzi condition.
Spurious pressure values come up when we use the non-staggered approximation for the velocity and pressure. However programming spectral methods (as I deal with the spectral collocation of the Stokes-equations) is hard for staggered-grids except the case when we apply homogeneous boundary...
Hi,
When we want to solve the Navier-Stokes equations coupled with the conservation of mass for incompressible fluids using the primitive-variable approach, we have to face to the problem that the equation for the continuity equation does not contain the pressure which leads to spurious...
Hi,
I would like to solve the steady-state incompressible Navier-Stokes equations by a spectral method. When I saw the classic primitive-variable finite element discretization of the time-dependent incompressible N-S, it turned out that the coefficient matrix of the derivatives of the unknowns...