836 research outputs found

    An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

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    We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated

    h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems

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    In this work we exploit agglomeration based hh-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature hh-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element L2L^2 projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.Comment: 78 pages, 7 figure

    High-order incompressible computational fluid dynamics on modern hardware architectures

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    In this thesis, a high-order incompressible Navier-Stokes solver is developed in the Python-based PyFR framework. The solver is based on the artificial compressibility formulation with a Flux Reconstruction (FR) discretisation in space and explicit dual time stepping in time. In order to reduce time to solution, explicit convergence acceleration techniques are developed and implemented. These techniques include polynomial multigrid, a novel locally adaptive pseudo-time stepping approach and novel stability-optimised Runge-Kutta schemes. Choices regarding the numerical methods and implementation are motivated as follows. Firstly, high-order FR is selected as the spatial discretisation due to its low dissipation and ability to work with unstructured meshes of complex geometries. Be- ing discontinuous, it also allows the majority of computation to be performed locally. Secondly, convergence acceleration techniques are restricted to explicit methods in order to retain the spatial locality provided by FR, which allows efficient harnessing of the massively parallel compute capability of modern hardware. Thirdly, the solver is implemented in the PyFR framework with cross-platform support such that it can run on modern heterogeneous systems via an MPI + X model, with X being CUDA, OpenCL or OpenMP. As such, it is well-placed to remain relevant in an era of rapidly evolving hardware architectures. The new software constitutes the first high-order accurate cross-platform imple- mentation of an incompressible Navier-Stokes solver via artificial compressibility. The solver and the convergence acceleration techniques are validated for a range of turbu- lent test cases. Furthermore, performance of the convergence acceleration techniques is assessed with a 2D cylinder test case, showing speed-up factors of over 20 relative to global RK4 pseudo-time stepping when all of the technologies are combined. Fi- nally, a simulation of the DARPA SUBOFF submarine model is undertaken using the solver and all convergence acceleration techniques. Excellent agreement with previ- ous studies is obtained, demonstrating that the technology can be used to conduct high-fidelity implicit Large Eddy Simulation of industrially relevant problems at scale using hundreds of GPUs.Open Acces

    Institute for Computational Mechanics in Propulsion (ICOMP)

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    The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

    A unified fractional-step, artificial compressibility and pressure-projection formulation for solving the incompressible Navier-Stokes equations

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    This paper introduces a unified concept and algorithm for the fractionalstep (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PP method has also been coupled with a non-linear, full-multigrid and full approximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems

    Modified HLLC-VOF solver for incompressible two-phase fluid flows

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    A modified HLLC-type contact preserving Riemann solver for incompressible two-phase flows using the artificial compressibility formulation is presented. Here, the density is omitted from the pressure evolution equation. Also, while calculating the eigenvalues and eigenvectors, the variations of the volume fraction is taken into account. Hence, the equations for the intermediate states and the intermediate wave speed are different from the previous HLLC-VOF formulation [Bhat S P and Mandal J C, J. Comput. Phys. 379 (2019), pp. 173-191]. Additionally, an interface compression algorithm is used in tandem to ensure sharp interfaces. The modified Riemann solver is found to be robust compared to the previous HLLC-VOF solver, and the results produced are superior compared to non-contact preserving solver. Several test problems in two- and three-dimensions are solved to evaluate the efficacy of the solver on structured and unstructured meshes

    Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

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    A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required

    A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

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    We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ=180Re_{\tau}=180 as well as 590590.Comment: 28 pages, in preparation for submission to Journal of Computational Physic

    Numerical solution of the incompressible Navier-Stokes equations

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    The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in psuedo-time for each physical time step. The system of equations is solved with a line-relaxation scheme which allows the use of very large pseudo-time steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. Numerous laminar test flow problems are computed and presented with a comparison against analytically known solutions or experimental results. These include the flow in a driven cavity, the flow over a backward-facing step, the steady and unsteady flow over a circular cylinder, flow over an oscillating plate, flow through a one-dimensional inviscid channel with oscillating back pressure, the steady-state flow through a square duct with a 90 degree bend, and the flow through an artificial heart configuration with moving boundaries. An adequate comparison with the analytical or experimental results is obtained in all cases. Numerical comparisons of the upwind differencing with central differencing plus artificial dissipation indicates that the upwind differencing provides a much more robust algorithm, which requires significantly less computing time. The time-dependent problems require on the order of 10 to 20 subiterations, indicating that the elliptical nature of the problem does require a substantial amount of computing effort
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