From the results of the numerical example, regularities were derived for the absolute value of the complex phase and group velocities on the complex plane.
Although most models require numerical techniques, the regularity and simplicity of this progression permitted an approximation by algebraic expressions.
In the traditional level set methods, in order to keep the regularity and numerical stability during the evolving process, periodical re-initialization [31 33] as a numeric remedy is introduced to maintain the level set function regularity.
It is then shown that there exists certain relationship between the problem of establishing if α∈R belongs to L or not and the numerical value of the regularity radius of the interval parametric matrix A(p)−αB(p).
In [11, 13], existence results in no-slip surface,, are obtained, while in [3, 7], Navier's slip conditions, and, are investigated, and numerical, existence, uniqueness, and regularity results are given.
Regularity is a numerical invariant that measures the complexity of the structure of homogeneous ideals in a polynomial ring.
Thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory.
In [8], Guo studied the existence, uniqueness, and regularity of the numerical solutions for the periodic initial value problem of generalized SRLW by the spectral method.
At the current state of research, higher-order elements p ≥ 2 formally require piecewise polynomial coefficients of L and additional regularity of f. □ Numerical examples for the symmetric case that underline the above result can be found in [49].
Third, the (near-wall) regularity of a solution of the Navier Stokes equations is numerically analyzed by means of Direct Numerical Simulation of turbulent channel flow performed with the staggered projection method.
