One of the visualization problems implies finding boundaries and insides of flat sections of 3D objects specified analytically. This problem is to be solved to analyze the results and to control the geometry specification. On the one hand, the analytic definition of profiles for “not simple” 3D-objects in general case is actually unsolvable problem; on the other hand, it is necessary to apply v...

We derive a bound on the order of accuracy of interpolation operators for energy stable summation-by-parts discretizations on non-conforming multiblock meshes. The new theoretical result, which corroborate with experience from previous work, implies a local reduction in the formal accuracy of summation-by-parts discretizations based on diagonal norms. Numerical results confirm a corresponding r...

This work concentrates upon the Mimetic discretization of elliptic partial differential equations (PDE). Numerical solutions are obtained and discussed for one-dimensional ODE on uniform and irregular grids and two-dimensional PDE on uniform grids. The focal point is to develop a scheme that incorporates the full tensor case on uniform grids in 2-D. The numerical results are then compared to pr...

Insight into the accuracy of steady shock-capturing CFD methods is obtained through analysis of a simple problem involving steady transonic ow in a quasi-1D diverging duct. It is proved that the discrete solution error on either side of the shock is O(h n) where n is the order of accuracy of the conservative nite volume discretisation. Furthermore, it is shown that provided that n 2 then the er...

We describe multi-material (more than two materials) interface reconstruction methods for 3D mesh of generalized polyhedrons. Basic information used in interface reconstruction is volume fractions of each material in mixed cell containing several materials. All methods subdivide mixed cell into set of pure non-overlapping sub-cells each containing just one material that have reference volume fr...

High-accuracy finite-difference schemes are used to solve the two-dimensional timedomain Maxwell equations for electromagnetic wave propagation and scattering. The high-accuracy schemes consist of a seven-point spatial operator coupled with a six-stage Runge–Kutta time-marching method. Two methods are studied, one of which produces the maximum order of accuracy and one of which is optimized for...

The hierarchical reconstruction (HR) [9, 20] is applied to a piecewise quadratic spectral volume method on two-dimensional unstructured grids as a limiting procedure to prevent spurious oscillations in numerical solutions. The key features of this HR are that the reconstruction on each control volume only uses adjacent control volumes, which forms a compact stencil set, and there is no truncati...

A postprocessing technique based on negative order norm estimates for the discontinuous Galerkin methods was previously introduced by Cockburn, Luskin, Shu, and Süli [Proceedings of the International Symposium on Discontinuous Galerkin Methods, Springer, New York, pp. 291– 300; Math. Comput., 72 (2003), pp. 577–606]. The postprocessor allows improvement in accuracy of the discontinuous Galerkin...

In many applications of ageand size-structured population models, there is an interest is obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Si...

We present a scheme for solving two-dimensional, nonlinear reaction-diiusion equations, s @p @t ? r (Krp) = f (p); using a mixed nite-element method. To linearize the mixed-method equations, we use a two grid scheme that relegates all of the Newton-like iterations to a grid 4H much coarser than the original one 4h, with no loss in order of accuracy so long as the mesh sizes obey H = O(p h). The...