Igor Menshov

Highly scalable implementation of an implicit matrix-free solver for gas dynamics on GPU-accelerated clusters

A numerical approach for solving gas dynamics on Cartesian grids is considered which employs an implicit time marching scheme with the matrix-free Lower-Upper Symmetric Gauss–Seidel (LU-SGS) method for solving discrete equations. Boundary conditions are treated with an embedded-boundary method. The method has two attractive features—(1) algorithmic uniformity of calculations and (2) structured memory accesses that well fit massively parallel architectures with GPU accelerators. We propose a novel CUDA+MPI computational algorithm scalable up to hundreds of GPUs and give in-depth analysis of its implementation (interoperability issues, libraries tuning).

Numerical modeling of elastoplastic flows by the Godunov method on moving Eulerian grids

The paper proposes a numerical method for calculating elastoplastic flows on adaptive Eulerian computational grids. Elastoplastic processes are described using the Prandtl-Reuss model. The spatial discretization of the Euler equations is carried out by the Godunov method on a moving grid. In order to improve the accuracy of the scheme, piecewise linear reconstruction of the grid functions is employed using a MUSCL-type interpolation scheme generalized to unstructured grids. The basic idea of the method is to split the system of governing equations into a hydrodynamic and an elastoplastic component. The hydrodynamic equations are solved by an absolutely stable explicit-implicit scheme, and the constitutive equations (elastoplastic component) are solved by a two-stage Runge-Kutta scheme. Theoretical analysis is performed and analytical solutions are obtained for a one-dimensional model describing the structures of a shock wave and a rarefaction wave in an elastoplastic material in the approximation of uniaxial strains. The proposed method is verified by the obtained analytical solutions and the solutions calculated using alternative approaches.

Efficient parallel shock-capturing method for aerodynamics simulations on body-unfitted cartesian grids

For problems with complex geometry, a numerical method is proposed for solving the three-dimensional nonstationary Euler equations on Cartesian grids with the use of hybrid computing systems. The baseline numerical scheme, a method for implementing internal boundary conditions on body-unfitted grids, and an iterative matrix-free LU-SGS method for solving the discretized equations are described. An efficient software implementation of the numerical algorithm on a multiprocessor hybrid CPU/GPU computing system is considered. Results of test computations are presented.

On Implementation High-Scalable CFD Solvers for Hybrid Clusters with Massively-Parallel Architectures

New approach for solving of compressible fluid dynamic problems with complex geometry on Cartesian grids is proposed. It leads to algorithmic uniformity for whole domain and structured memory accesses which are essential for effective implementations on massively-parallel architectures --- GPUs. Methods used are based on implicit scheme and LU-SGS method. Novel parallel algorithm for last one is proposed. In-depth analysis of CUDA+MPI implementation interoperability issues, libraries tuning scalable upi¾?to hundreds GPUs is performed.

Towards understanding the physics of supersonic jet screech

Jet flows have been a subject of intensive theoretical, numerical, and experimental investigations during last several decades. Many fluid dynamicists and specialists in computer simulations have endeavored to learn more about very complicated structures in jet flows. This interest have been in the first turn feeding by the desire to understand basic mechanisms of strong noise generated by high-speed jets, in particular very intense tones known as jet screech.

Tearing instability of isolated compressible vortices

The present paper addresses the instability of a compressible vortex flow. We consider a family of so-called isolated vortices – the circular planar vortices that have zero circulation (net vorticity). The term “isolation” implies the presence of a shield in the vorticity field – a region of vorticity of common sign surrounding the central domain where the vorticity is oppositely signed. To model such a vorticity field, a generalized Taylor-type profile for the swirl velocity in the radial direction is employed, which involves two parameters: intensity μ (proportional to the maximal velocity) and steepness β (characterizing the scale of the shield zone). Vortices are assumed to be compressible and homentropic. The linear-stability analysis is carried out, which shows that isolated vortices can exhibit both stable and unstable behavior depending on the model parameters μ and β. By numerical simulations of the non-linear stage, the unstable normal modes are shown to evolve towards tearing of the basic vortex with formation of smaller secondary vortical structures.

A Parallel Locally-Adaptive 3D Model on Cartesian Nested-Type Grids

The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and its software implementation in an application library written in C++ object-oriented language with the application program interface OpenMP for parallelizing calculations on shared memory. The library accounts for the specifics of multithread calculations of 3D problems on Cartesian grids, which makes it possible to substantially minimize the loaded memory via non-storing the grid information. The loop order over cells is represented by a special list that remarkably simplifies parallel realization with the OpenMP directives. Test results show high effectiveness of dynamical local adaptation of Cartesian grids, and increasing of this effectiveness while the number of adaptation levels becomes larger.

Parallel Algorithms for an Implicit CFD Solver on Tree-Based Grids

Parallel implementation of the implicit LU-SGS solver is considered. It leads to the graph coloring problem. A novel recursive graph coloring algorithm has been proposed that requires only three colors on 2:1 balanced quadtree-based meshes. The algorithm has been shown to allow simple parallel implementations, including GPU architectures, and is fully coherent with local grid coarsing/refining procedures resulting in highly effective co-execution with local grid adaptation.

The effect of incident flow on a supersonic circumfluence of a blunt object

The influence of the inhomogeneity of a narrow wake with a reduced Mach number and total pressure values on the circumfluence about a blunt body (truncated cone) has been investigated. Two variants in the wake formation have been considered: behind the energy source and behind the moving body. A free boundary method was used for the flow simulation about moving bodies (a variant of the immersed boundary method). The dynamics of the moving body interaction with the head shock wave and formation of the reverse flow region have been studied. For consideration of these modes, it is shown that the presence of the wake before the front part of the body leads to a considerable decrease of wave resistance.

Exact and approximate Riemann solvers for compressible two-phase flows

Numerical methods for solving equations of two-phase hydrodynamics, which describe the flow of a dispersed solid and gas mixture are considered. The Godunov method is applied as the main approach to approximate numerical fluxes in solutions of the relevant Riemann problems. The formulations of these problems for the solid and gas phases are given, their exact analytical solution is described, and possible simplified approximate solutions are discussed. The obtained theoretical results are applied to the construction of a discrete model, which results in the generalization of the well-known Godunov-type and Rusanov-type methods to the case of nonequilibrium two-phase media. The numerical results involve the verification of the constructed methods on the analytical solutions of two-phase equations.