This paper describes multi-thread parallel open source JAVA implementation of alternating directions isogeometric L2 projections solver. The solver enables for fast numerical simulations of time-dependent problems. To apply our solver, the time-dependent problem must be discretized using isogeometric finite element method with B-spline basis functions in the spatial domain. The problem is solve...

Heat transfer in a Rayleigh-Bénard configuration consisting of a vertical cylinder, which is rotating about its axis, can be intensified considerably when the rotation rate is modulated harmonically in time. Such time-dependent rotation introduces an Euler force into the governing equations which leads to a particular modification of the flow that is shown to support a Nusselt number (Nu) that ...

We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering meth...

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing sol...

The classical two-phase Stefan problem in level set formulation is considered. The implementation of a solver on triangular grids is described. Extended finite elements (X-FEM) in space and an implicit Euler method in time are used to approximate the temperature. For the level set equation, a discontinuous Galerkin (DG) and a strong stability preserving (SSP) RungeKutta scheme are employed. Pol...

All speed flows and in particular low Mach number flow algorithms are addressed for the numerical approximation of the Kapila et al. [19] multiphase flow model. This model is valid for fluid mixtures evolving in mechanical equilibrium but out of temperature equilibrium and is efficient for material interfaces computation separating miscible and non-miscible fluids. In this context, the interfac...

numerical analyses have shown that successful flow simulations and the accuracy of solution noticeably depend on the number of nodes used in computational meshing. a suitable meshing should have the capability of adapting with main flow parameters. because the number of total nodes that can be used in numerical simulation is limited, making such grid for complex flows is almost difficult, if it...

where Ω ⊂ R, ∂ΩD ∪ ∂ΩN = ∂Ω and the two boundary regions are distinct with ∂ΩD non-empty. Specifically, we will consider the key results in the development of the theory of finite elements, including weak solutions and the structure of the individual elements, as well as the numerical implementation of the method. We will subsequently implement a finite element numerical solver in order to solv...

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation h...

This paper deals with a numerical method for an airfoil design. It is shown how to create an airfoil from a given velocity distribution along a mean camber line. The method is based on searching a fixed point of a contractive operator. We need to have a fast solver of the Euler equations. The Newton method for solving implicit finite volume scheme is described. The resulting system of linear al...