An Adaptive Sparse Grid Navier Stokes Solver in 3d Based on the Finite Diierence Method
نویسندگان
چکیده
Sparse grids provide an eecient representation of discrete solutions of PDEs and are mainly based on speciic tensor products of 1D hierarchical basis ansatz functions. They easily allow adaptive reenement and coarsening. We present special nite diierences on sparse grids which possess nearly the same properties as nite diierences on full grids. Also higher order nite diierence operators on sparse grids can easily be obtained. Using this approach, partial diierential equations of second order can be discretized straightforwardly. These techniques are employed within a procedure for the solution of the Navier Stokes equations in 3D. Here, we apply the method of artiicial compressibility and a pressure correction method.
منابع مشابه
Scientific Flow Field Simulation of Cruciform Missiles Through the Thin Layer Navier Stokes Equations
The thin-layer Navier-Stokes equations are solved for two complete missile configurations on an IBM 3090-200 vectro-facility supercomputer. The conservation form of the three-dimensional equations, written in generalized coordinates, are finite differenced and solved on a body-fitted curvilinear grid system developed in conjunction with the flowfield solver. The numerical procedure is based on ...
متن کاملA Fast Solver for Incompressible Navier-stokes Equations with Finite Difference Methods
In this paper, a fast direct solver for incompressible Navier-Stokes equations with nite diierence methods on the half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-deenite pair are developed. Our fast solver can also be extended to three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed.
متن کاملAn Incompressible Navier-Stokes Equations Solver on the GPU Using CUDA Master of Science Thesis in Complex Adaptive Systems
Graphics Processing Units (GPUs) have emerged as highly capable computational accelerators for scientific and engineering applications. Many reports claim orders of magnitude of speedup compared to traditional Central Processing Units (CPUs), and the interest for GPU computation is high in the computational world. In this thesis, the capability of using GPUs to accelerate the full computational...
متن کامل46. G. Wittum. Multi-grid Methods for Stokes and Navier-stokes Equations with Transform- Ing Smoothers: Algorithms and Numerical Results. Gmres: a Generalized Minimal Residual Algorithm for Solving Non-symmetric Linear Systems.grid and Iccg for Problems with Interfaces. In
Numerical solution of the stationary navier-stokes equations by means of a multiple grid method and newton iteration. Distributive iterationen f ur indeenite Systeme als Gll atter in Mehrgitter-verfahren am Beispiel der Stokes-und Navier-Stokes-Gleichungen mit Schwerpunkt auf unvollstt andingen Zerlegungen. PhD thesis, Christan-Albrechts Universitt at, Kiel, 1986. 145. G. Wittum. Linear iterati...
متن کاملA Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...
متن کامل