Sentence examples for divergence space from inspiring English sources

The divergence space used in this context is defined by boldsymbol{W}= H operatorname {div} Omega)= bigl{ boldsymbol{q}in L^{2}( Omega)^{2}; operatorname {div}boldsymbol{q}in L^{2}(Omega) bigr} with norm (Vert boldsymbol{q}Vert _{boldsymbol{W}}=[Vert boldsymbol{q}Vert _{0}^{2}+Vert operatorname {div}boldsymbol{q}Vert _{0}^{2}]^{1/2}).

A simple method for preserving divergence-free is obtained by projecting the velocity onto the divergence-free space after generating the new mesh at the last iterative step.

The divergence-free space (V_{h}) is introduced only for theoretical analysis.

A novel projection of vorticity onto the divergence-free space and its application to the two approaches are studied.

In doing so, a Poisson equation needs to be solved at each time-step to project the velocity field onto a divergence-free space.

The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection.

The resulting gradient, curl and divergence conforming spaces have the property that the conservation laws become completely independent of the basis functions.

In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space.

Since the divergence-free space (V_{h}subset X_{h}), we can define the norms of the dual spaces (X_{h}), (V_{h}) by Vert omega Vert _{X_{h}^=sup_{mathbf{v}_{h}in X_{h}} frac{(omega,mathbf{v}_{h})}{ Vert nablamathbf{v}_{h} Vert },qquad Vert omega Vert _{V_{h}^=sup _{mathbf{v}_{h}in V_{h}}frac{(omega,mathbf{v}_{h})}{ Vert nablamathbf{v}_{h} Vert }. [36 38].

In particular, our results can be applied to relaxation and minimization problems in BV, BD and divergence-free spaces.

Species today face many challenges that influence their genetic, phenotypic, and ecological diversity and divergence patterns across space and time.