Recent content by defunc

In many cfd textbooks the domain of dependence is stated as the entire region emclosed by the characteristics. Is this correct? Isnt it only the values on the characteristics? Thanks!

Hi, Does the following inequality hold regarding the product of 2 matrices A and B: p(AB) <= p(A)p(B), where p denotes the spectral radius. Thanks!

Hi there, I have a system of 2n equations. n of these unknowns can be expressed explicitly in terms of the remaining n. The resulting n x n matrix is more dense than the original 2n x 2n and the original 2n x 2n system has some desired properties like diagonal dominance etc. So, should I...

its a fixed point iteration scheme. this specific case you can derive from Newtons method to find the zeros of x^2-2.

hi there. a sufficient condition is that the derivative in the fixed point has to be smaller than one in absolute value

Hi In the spectral method, the Fourier series is differentiated term by term. How do we know this series converges uniformly to the real derivative? Or can it be shown in general for fouries series? Thanks a lot!

Are there any variations of Newtons method, say where you use higher derivatives?

As long as it forms a basis, I don't think it matters. So the basis functions youre used to should work here as well. I suggest using a weak form if you have Neumann boundaries.

Hi all, Suppose the solution of a pde exists and is unique, what can be said about the smoothness thereof? In general, is there some theory regarding the smoothness of the solution and its derivatives and how it depends on the boundary and boundary values? For example, if the boundary values...

Probably unit related. The equation for delta_p(your second equation) will have units in pascal.

I'm sure that was clear to everyone...

Guess a constant vector for the particular solution. This will give x_{p}=(I-A)^{-1}b Then add it to the homogeneous solution to obtain the solution.

The equations you gave is also based on an assumption: perfect gas behaviour. So its not applicable to any fluids. So my question still remains, under the assumption of incompressible flow, what's the relation between total and static temperatures? Is it the same?

Both have to be invertible. Inv(AB) = inv(B)inv(A).

Mingers equations are based on perfect gas laws. For incompressible flow entropy is only a function of temperature. From there my conclusion...