arXiv subjects

Anand Radhakrishnan

Publications and source records attributed to Anand Radhakrishnan.

11 recordsLinked to original sources

arXiv2026

A sub-grid-scale model for polydisperse bubbly flows with heat and mass transfer

Ensemble-averaged models of polydisperse bubbly flows require statistics of the evolving bubble population. Prior quadrature-based moment formulations close bubble pressure with a polytropic relation that omits heat and mass transfer at the bubble wall. We formulate constant-transfer equations for bubble pressure and vapor mass within a conditional hyperbolic quadrature method. Second-order conditional inversion produces four joint radius--radial-velocity nodes per equilibrium-radius bin. Bubble pressure and vapor mass are advanced at each node. The node values close the ensemble-averaged flow equations without adding mixed pressure or vapor-mass moments to the transported moment set. The model is implemented in MFC. Monte Carlo calculations verify the evolution of quadrature nodes and the mean bubble variables for a harmonically forced population. Bubble-screen calculations quantify closure error as the equilibrium radius is discretized and the initial distributions vary. The constant-transfer calculation does not exhibit the high-frequency pressure oscillations observed with the polytropic closure under the conditions considered. 3D bubble-screen calculations give a 1.5% relative root-mean-square error between the Euler--Euler center pressure and the mean of 40 volume-averaged Euler--Lagrange realizations.

physics.flu-dyn↗

arXiv2026

Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier--Stokes-like problems

Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs--Runge oscillations that result from traditional numerics. These approaches face a delicate balance in achieving sufficiently regular solutions without dissipating fine-scale features, such as turbulence or acoustics. Recent work by Cao and Sch\"afer introduces information geometric regularization (IGR), the first inviscid regularization method for fluid dynamics. IGR replaces shock singularities with smooth profiles of adjustable width, without dissipating fine-scale features. This work provides a strategy for the practical use of IGR in finite-volume-based numerical methods. We illustrate its performance on canonical test problems and compare it against established approaches based on limiters and Riemann solvers. Results show that the finite volume IGR approach recovers the expected solutions in all cases. Across canonical benchmarks, IGR achieves accuracy competitive with WENO and LAD shock-capturing schemes in both smooth and discontinuous flow regimes. The IGR approach is computationally light, with meaningfully fewer memory accesses and arithmetic operations per time step.

cs.CE↗

arXiv2025

Testing and benchmarking emerging supercomputers via the MFC flow solver

Deploying new supercomputers requires testing and evaluation via application codes. Portable, user-friendly tools enable evaluation, and the Multicomponent Flow Code (MFC), a computational fluid dynamics (CFD) code, addresses this need. MFC is adorned with a toolchain that automates input generation, compilation, batch job submission, regression testing, and benchmarking. The toolchain design enables users to evaluate compiler-hardware combinations for correctness and performance with limited software engineering experience. As with other PDE solvers, wall time per spatially discretized grid point serves as a figure of merit. We present MFC benchmarking results for five generations of NVIDIA GPUs, three generations of AMD GPUs, and various CPU architectures, utilizing Intel, Cray, NVIDIA, AMD, and GNU compilers. These tests have revealed compiler bugs and regressions on recent machines such as Frontier and El Capitan. MFC has benchmarked approximately 50 compute devices and 5 flagship supercomputers.

cs.DC↗

arXiv2025

Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques along computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU--GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation on well-conditioned numerics is used. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is seen on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8-node baseline and stretching to the full system.

physics.comp-ph↗

arXiv2025

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work, MFC 3.0, was published, documented, and made open-source by Bryngelson et al. CPC (2021) features numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. We exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF's Frontier and LLNL's El Capitan. Combined with MFC's single-accelerator performance, MFC achieves exascale computation in practice and has achieved the largest-to-date public CFD simulation at 200 trillion grid points, earning it a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, $N$-fluid phase change, Euler-Euler and Euler-Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF's Summit and Frontier, and LLNL's El Capitan, achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-fold increase in device count show parallel efficiencies exceeding 90% on OLCF Frontier.

physics.flu-dyn↗

arXiv2024

OpenACC offloading of the MFC compressible multiphase flow solver on AMD and NVIDIA GPUs

GPUs are the heart of the latest generations of supercomputers. We efficiently accelerate a compressible multiphase flow solver via OpenACC on NVIDIA and AMD Instinct GPUs. Optimization is accomplished by specifying the directive clauses 'gang vector' and 'collapse'. Further speedups of six and ten times are achieved by packing user-defined types into coalesced multidimensional arrays and manual inlining via metaprogramming. Additional optimizations yield seven-times speedup in array packing and thirty-times speedup of select kernels on Frontier. Weak scaling efficiencies of 97% and 95% are observed when scaling to 50% of Summit and 95% of Frontier. Strong scaling efficiencies of 84% and 81% are observed when increasing the device count by a factor of 8 and 16 on V100 and MI250X hardware. The strong scaling efficiency of AMD's MI250X increases to 92% when increasing the device count by a factor of 16 when GPU-aware MPI is used for communication.

physics.flu-dyn↗

arXiv2023

Method for portable, scalable, and performant GPU-accelerated simulation of multiphase compressible flow

Multiphase compressible flows are often characterized by a broad range of space and time scales. Thus entailing large grids and small time steps, simulations of these flows on CPU-based clusters can thus take several wall-clock days. Offloading the compute kernels to GPUs appears attractive but is memory-bound for standard finite-volume and -difference methods, damping speed-ups. Even when realized, faster GPU-based kernels lead to more intrusive communication and I/O times. We present a portable strategy for GPU acceleration of multiphase compressible flow solvers that addresses these challenges and obtains large speedups at scale. We use OpenACC for portable offloading of all compute kernels while maintaining low-level control when needed. An established Fortran preprocessor and metaprogramming tool, Fypp, enables otherwise hidden compile-time optimizations. This strategy exposes compile-time optimizations and high memory reuse while retaining readable, maintainable, and compact code. Remote direct memory access, realized via CUDA-aware MPI, reduces communication times. We implement this approach in the open-source solver MFC. Metaprogramming-based preprocessing results in an 8-times speedup of the most expensive kernels, 46% of peak FLOPs on NVIDIA GPUs, and high arithmetic intensity (about 10 FLOPs/byte). In representative simulations, a single A100 GPU is 300-times faster than an Intel Xeon CPU core, corresponding to a 9-times speedup for a single A100 compared to the entire CPU die. At the same time, near-ideal (97%) weak scaling is observed for at least 13824 GPUs on Summit. A strong scaling efficiency of 84% is retained for an 8-times increase in GPU count. Collective I/O, implemented via MPI3, helps ensure negligible contribution of data transfers. Large many-GPU simulations of compressible (solid-)liquid-gas flows demonstrate the practical utility of this strategy.

physics.flu-dyn↗

arXiv2022

Application Experiences on a GPU-Accelerated Arm-based HPC Testbed

This paper assesses and reports the experience of ten teams working to port,validate, and benchmark several High Performance Computing applications on a novel GPU-accelerated Arm testbed system. The testbed consists of eight NVIDIA Arm HPC Developer Kit systems built by GIGABYTE, each one equipped with a server-class Arm CPU from Ampere Computing and A100 data center GPU from NVIDIA Corp. The systems are connected together using Infiniband high-bandwidth low-latency interconnect. The selected applications and mini-apps are written using several programming languages and use multiple accelerator-based programming models for GPUs such as CUDA, OpenACC, and OpenMP offloading. Working on application porting requires a robust and easy-to-access programming environment, including a variety of compilers and optimized scientific libraries. The goal of this work is to evaluate platform readiness and assess the effort required from developers to deploy well-established scientific workloads on current and future generation Arm-based GPU-accelerated HPC systems. The reported case studies demonstrate that the current level of maturity and diversity of software and tools is already adequate for large-scale production deployments.

cs.DC↗

arXiv2021

A High-Order Accurate Meshless Method for Solution of Incompressible Fluid Flow Problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or elements, issues such as grid skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse Multiquadrics are some of the most popular RBFs used for the solutions of fluid flow and heat transfer problems. But they have additional shape parameters that have to be fine tuned for accuracy and stability. Moreover, they also face stagnation error when the point density is increased for accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials. In this research, we extend the PHS-RBF method for the solution of incompressible Navier-Stokes equations. A fractional step method with explicit convection and explicit diffusion terms is combined with a pressure Poisson equation to satisfy the momentum and continuity equations. Systematic convergence tests have been performed for five model problems with two of them having analytical solutions. We demonstrate fast convergence both with refinement of number of points and degree of appended polynomials. The method is further applied to solve problems such as lid-driven cavity and vortex shedding over circular cylinder. We have also analyzed the performance of this approach for solution of Euler equations. The proposed method shows promise to solve fluid flow and heat transfer problems in complex domains with high accuracy.

math.NA↗

arXiv2021

A Non-Nested Multilevel Method for Meshless Solution of the Poisson Equation in Heat Transfer and Fluid Flow

We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve exponential convergence of discretization errors. The interpolations are performed over local clouds of points and the Poisson equation is collocated at each of the scattered points, resulting in a sparse set of discrete equations for the unkown variables. To solve this set of equations, we have developed a non-nested multilevel algorithm utilizing multiple independently generated coarse sets of points. The restriction and prolongation operators are also constructed with the same RBF interpolations procedure. The performance of the algorithm for Dirichlet and all-Neumann boundary conditions is evaluated in three model geometries using a manufactured solution. For Dirichlet boundary conditions, rapid convergence is observed using SOR point solver as the relaxation scheme. For cases of all-Neumann boundary conditions, convergence is seen to slow down with the degree of the appended polynomial. However, when the multilevel procedure is combined with a GMRES algorithm, the convergence is seen to significantly improve. The GMRES accelerated multilevel algorithm is included in a fractional step method to solve incompressible Navier-Stokes equations.

math.NA↗

arXiv2019

Diffusion approximations and control variates for MCMC

A new methodology is presented for the construction of control variates to reduce the variance of additive functionals of Markov Chain Monte Carlo (MCMC) samplers. Our control variates are definedthrough the minimization of the asymptotic variance of the Langevin diffusion over a family of functions, which can be seen as a quadratic risk minimization procedure. The use of these control variates is theoretically justified. We show that the asymptotic variances of some well-known MCMC algorithms, including the Random Walk Metropolis and the (Metropolis) Unadjusted/Adjusted Langevin Algorithm, are close to the asymptotic variance of the Langevin diffusion. Several examples of Bayesian inference problems demonstrate that the corresponding reduction in the variance is significant.

stat.ME↗