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  1. Z

    Associativity of Hadamard and matrix product

    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...
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    Work done by gravity - what is wrong?

    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...
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    Determine particle position knowing the velocity field

    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...
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    Why incompressible fluid flow is advantageous in numerical computation

    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...
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    Steady-state incompressible Navier-Stokes discretization

    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...
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    What is the advantage of Hamilton's canonical equations?

    Hi! I would like to know that in what circumstances Hamilton's canonical equations are superior to the Lagrange-equations of the second kind. We know that every second order equation can be rewritten as a system of first order equations. Thanks, Zoli
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    Dimensional Analysis with non-dimensional initial parameter

    I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.)...