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Prabhu Ramachandran

Publications and source records attributed to Prabhu Ramachandran.

At least 19 recordsLinked to original sources

Rapid Variable Resolution Particle Initialization for Complex Geometries

The accuracy of meshless methods like Smoothed Particle Hydrodynamics (SPH) is highly dependent on the quality of the particle distribution. Existing particle initialization techniques often struggle to simultaneously achieve adaptive resolution, handle intricate boundaries, and efficiently generate well-packed distributions inside and outside a boundary. This work presents a fast and robust particle initialization method that achieves these goals using standard SPH building blocks. Our approach enables simultaneous initialization of fluid and solid regions, supports arbitrary geometries, and achieves high-quality, quasi-uniform particle arrangements without complex procedures like surface bonding. Extensive results in both 2D and 3D demonstrate that the obtained particle distributions exhibit good boundary conformity, low spatial disorder, and minimal density variation, all with significantly reduced computational cost compared to existing approaches. This work paves the way for automated particle initialization to accurately model flow in and around bodies with meshless methods, particularly with SPH.

physics.comp-ph

Adaptive Compressible Smoothed Particle Hydrodynamics

Modulating the number of particles in a region is key to accurately capturing the nuances in compressible flows with Smoothed Particle Hydrodynamics (SPH). This paper presents a volume-based adaptive refinement and derefinement procedure, with state-of-the-art features such as automatic local adaptivity and solution adaptivity applied in the context of compressible flows. A shock-aware particle shifting procedure is introduced to regularize the particle distribution while preserving the integrity of shocks. To our knowledge, this is the first demonstration of shock-based solution adaptivity and shock-aware particle shifting in the literature. A wide variety of test problems, which involve flow in and around boundaries, are employed to highlight the utility of these adaptivity features in improving the results and in making simulations faster. For instance, the adaptive resolution procedure is shown to achieve an order of magnitude increase in computational speed. We also demonstrate the effectiveness of the adaptivity procedure in resolving issues such as errors arising from the interaction with differently spaced ghost particles at boundaries, formation of spot-like structures due to particle clumping, and poorly resolved low-density regions. In essence, the adaptivity technique presented in this paper is a powerful tool for simulating compressible flows with enhanced accuracy and efficiency.

physics.flu-dyn

Robust Solid Boundary Treatment for Compressible Smoothed Particle Hydrodynamics

The unavailability of accurate boundary treatment methods for compressible Smoothed Particle Hydrodynamics (SPH) severely limits its ability to simulate flows in and around bodies. To this end, challenges specific to compressible flows with SPH are carefully considered. Based on these, robust and widely applicable boundary treatment methods for compressible SPH are proposed. These are accompanied by a novel technique to prevent particle penetration at boundaries. The proposed methods are shown to be significantly better than other recent approaches. A wide variety of test problems, many of which are not shown to be simulated with SPH thus far, are employed to highlight the strengths and weaknesses of the proposed methods. The implementation is open source and the results are automated in the interest of reproducibility. Overall, this research contributes to the advancement of SPH as a viable alternative to mesh-based methods for compressible flow simulations.

physics.flu-dyn

A Second-Order, Variable-Resolution, Weakly-Compressible Smoothed Particle Hydrodynamics Scheme

The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp gradients in the flow have also been developed. However, most of the SPH schemes in the literature are not second-order convergent (SOC). Both second-order convergence and adaptive resolution are considered grand challenge problems in the SPH community. In this paper, we propose, for the first time, a second-order convergent (SOC) adaptive refinement strategy along with a SOC weakly-compressible SPH scheme. We employ the method of manufactured solutions to systematically develop the scheme and validate the solver. We demonstrate the order of convergence of the entire scheme using the Taylor-Green vortex problem and then go on to demonstrate the applicability of the method to simulate flow past a circular cylinder.

physics.flu-dyn

Science with the Daksha High Energy Transients Mission

We present the science case for the proposed Daksha high energy transients mission. Daksha will comprise of two satellites covering the entire sky from 1~keV to $>1$~MeV. The primary objectives of the mission are to discover and characterize electromagnetic counterparts to gravitational wave source; and to study Gamma Ray Bursts (GRBs). Daksha is a versatile all-sky monitor that can address a wide variety of science cases. With its broadband spectral response, high sensitivity, and continuous all-sky coverage, it will discover fainter and rarer sources than any other existing or proposed mission. Daksha can make key strides in GRB research with polarization studies, prompt soft spectroscopy, and fine time-resolved spectral studies. Daksha will provide continuous monitoring of X-ray pulsars. It will detect magnetar outbursts and high energy counterparts to Fast Radio Bursts. Using Earth occultation to measure source fluxes, the two satellites together will obtain daily flux measurements of bright hard X-ray sources including active galactic nuclei, X-ray binaries, and slow transients like Novae. Correlation studies between the two satellites can be used to probe primordial black holes through lensing. Daksha will have a set of detectors continuously pointing towards the Sun, providing excellent hard X-ray monitoring data. Closer to home, the high sensitivity and time resolution of Daksha can be leveraged for the characterization of Terrestrial Gamma-ray Flashes.

astro-ph.HE

Daksha: On Alert for High Energy Transients

We present Daksha, a proposed high energy transients mission for the study of electromagnetic counterparts of gravitational wave sources, and gamma ray bursts. Daksha will comprise of two satellites in low earth equatorial orbits, on opposite sides of earth. Each satellite will carry three types of detectors to cover the entire sky in an energy range from 1 keV to >1 MeV. Any transients detected on-board will be announced publicly within minutes of discovery. All photon data will be downloaded in ground station passes to obtain source positions, spectra, and light curves. In addition, Daksha will address a wide range of science cases including monitoring X-ray pulsars, studies of magnetars, solar flares, searches for fast radio burst counterparts, routine monitoring of bright persistent high energy sources, terrestrial gamma-ray flashes, and probing primordial black hole abundances through lensing. In this paper, we discuss the technical capabilities of Daksha, while the detailed science case is discussed in a separate paper.

astro-ph.IM

Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such shortcomings are (i) their computational inefficiency relative to classical numerical methods, and (ii) the non-interpretability of a trained DNN model. In this work we present ASPINN, an anisotropic extension of our earlier work called SPINN--Sparse, Physics-informed, and Interpretable Neural Networks--to solve PDEs that addresses both these issues. ASPINNs generalize radial basis function networks. We demonstrate using a variety of examples involving elliptic and hyperbolic PDEs that the special architecture we propose is more efficient than generic DNNs, while at the same time being directly interpretable. Further, they improve upon the SPINN models we proposed earlier in that fewer nodes are require to capture the solution using ASPINN than using SPINN, thanks to the anisotropy of the local zones of influence of each node. The interpretability of ASPINN translates to a ready visualization of their weights and biases, thereby yielding more insight into the nature of the trained model. This in turn provides a systematic procedure to improve the architecture based on the quality of the computed solution. ASPINNs thus serve as an effective bridge between classical numerical algorithms and modern DNN based methods to solve PDEs. In the process, we also streamline the training of ASPINNs into a form that is closer to that of supervised learning algorithms.

cs.LG

How to train your solver: Verification of boundary conditions for smoothed particle hydrodynamics

The weakly compressible smoothed particle hydrodynamics (WCSPH) method has been employed to simulate various physical phenomena involving fluids and solids. Various methods have been proposed to implement the solid wall, inlet/outlet, and other boundary conditions. However, error estimation and the formal rates of convergence for these methods have not been discussed or examined carefully. In this paper, we use the method of manufactured solution (MMS) to verify the convergence properties of a variety of commonly employed of various solid, inlet, and outlet boundary implementations. In order to perform this study, we propose various manufactured solutions for different domains. On the basis of the convergence offered by these methods, we systematically propose a convergent WCSPH scheme along with suitable methods for implementing the boundary conditions. We also demonstrate the accuracy of the proposed scheme by using it to solve the flow past a circular cylinder. Along with other recent developments in the use of adaptive resolution, this paves the way for accurate and efficient simulation of incompressible or weakly-compressible fluid flows using the SPH method.

math.NA

Efficient and Accurate Adaptive Resolution for Weakly-Compressible SPH

In this paper we propose an accurate, and computationally efficient method for incorporating adaptive spatial resolution into weakly-compressible Smoothed Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged in an accurate manner. Critically, the method ensures that the number of neighbors of each particle is optimal, leading to an efficient algorithm. A set of background particles is used to specify either geometry-based spatial resolution, where the resolution is a function of distance to a solid body, or solution-based adaptive resolution, where the resolution is a function of the computed solution. This allows us to simulate problems using particles having length variations of the order of 1:250 with much fewer particles than currently reported with other techniques. The method is designed to automatically adapt when any solid bodies move. The algorithms employed are fully parallel. We consider a suite of benchmark problems to demonstrate the accuracy of the approach. We then consider the classic problem of the flow past a circular cylinder at a range of Reynolds numbers and show that the proposed method produces accurate results with a significantly reduced number of particles. We provide an open source implementation and a fully reproducible manuscript.

physics.flu-dyn

Parallel adaptive weakly-compressible SPH for complex moving geometries

The use of adaptive spatial resolution to simulate flows of practical interest using Smoothed Particle Hydrodynamics (SPH) is of considerable importance. Recently, Muta and Ramachandran [1] have proposed an efficient adaptive SPH method which is capable of handling large changes in particle resolution. This allows the authors to simulate problems with much fewer particles than was possible earlier. The method was not demonstrated or tested with moving bodies or multiple bodies. In addition, the original method employed a large number of background particles to determine the spatial resolution of the fluid particles. In the present work we establish the formulation's effectiveness for simulating flow around stationary and moving geometries. We eliminate the need for the background particles in order to specify the geometry-based or solution-based adaptivity and we discuss the algorithms employed in detail. We consider a variety of benchmark problems, including the flow past two stationary cylinders, flow past different NACA airfoils at a range of Reynolds numbers, a moving square at various Reynolds numbers, and the flow past an oscillating cylinder. We also demonstrate different types of motions using single and multiple bodies. The source code is made available under an open source license, and our results are reproducible.

physics.flu-dyn

Techniques for second order convergent weakly-compressible smoothed particle hydrodynamics schemes without boundaries

Despite the many advances in the use of weakly-compressible smoothed particle hydrodynamics (SPH) for the simulation of incompressible fluid flow, it is still challenging to obtain second-order convergence even for simple periodic domains. In this paper we perform a systematic numerical study of convergence and accuracy of kernel-based approximation, discretization operators, and weakly-compressible SPH (WCSPH) schemes. We explore the origins of the errors and issues preventing second-order convergence despite having a periodic domain. Based on the study, we propose several new variations of the basic WCSPH scheme that are all second-order accurate. Additionally, we investigate the linear and angular momentum conservation property of the WCSPH schemes. Our results show that one may construct accurate WCSPH schemes that demonstrate second-order convergence through a judicious choice of kernel, smoothing length, and discretization operators in the discretization of the governing equations.

math.NA

A corrected transport-velocity formulation for fluid and structural mechanics with SPH

Particle shifting techniques (PST) have been used to improve the accuracy of the Smoothed Particle Hydrodynamics (SPH) method. Shifting ensures that the particles are distributed homogeneously in space. This may be performed by moving the particles using a transport velocity. In this paper, we propose an extension to the class of Transport Velocity Formulation (TVF) methods. We derive the equations in a consistent manner and show that there are additional terms that significantly improve the accuracy of the method. In particular, we apply this to the Entropically Damped Artificial Compressibility SPH method. We identify the free-surface particles and their normals using a simple approach and thereby adapt the method for free-surface problems. We show how the new method can be applied to the problem of elastic dynamics. We consider a suite of benchmark problems involving both fluid and solid mechanics to demonstrate the accuracy and applicability of the method. The implementation is open source, and the manuscript is fully reproducible.

physics.flu-dyn

How to train your solver: A method of manufactured solutions for weakly-compressible SPH

The Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) method is a Lagrangian method that is typically used for the simulation of incompressible fluids. While developing an SPH-based scheme or solver, researchers often verify their code with exact solutions, solutions from other numerical techniques, or experimental data. This typically requires a significant amount of computational effort and does not test the full capabilities of the solver. Furthermore, often this does not yield insights on the convergence of the solver. In this paper we introduce the method of manufactured solutions (MMS) to comprehensively test a WCSPH-based solver in a robust and efficient manner. The MMS is well established in the context of mesh-based numerical solvers. We show how the method can be applied in the context of Lagrangian WCSPH solvers to test the convergence and accuracy of the solver in two and three dimensions, systematically identify any problems with the solver, and test the boundary conditions in an efficient way. We demonstrate this for both a traditional WCSPH scheme as well as for some recently proposed second order convergent WCSPH schemes. Our code is open source and the results of the manuscript are reproducible.

physics.flu-dyn

SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs we develop a class of sparse neural network architectures that are partially interpretable. The SPINN model we propose here serves as a seamless bridge between two extreme modeling tools for PDEs, namely dense neural network based methods like Physics Informed Neural Networks (PINNs) and traditional mesh-free numerical methods, thereby providing a novel means to develop a new class of hybrid algorithms that build on the best of both these viewpoints. A unique feature of the SPINN model that distinguishes it from other neural network based approximations proposed earlier is that it is (i) interpretable, in a particular sense made precise in the work, and (ii) sparse in the sense that it has much fewer connections than typical dense neural networks used for PDEs. Further, the SPINN algorithm implicitly encodes mesh adaptivity and is able to handle discontinuities in the solutions. In addition, we demonstrate that Fourier series representations can also be expressed as a special class of SPINN and propose generalized neural network analogues of Fourier representations. We illustrate the utility of the proposed method with a variety of examples involving ordinary differential equations, elliptic, parabolic, hyperbolic and nonlinear partial differential equations, and an example in fluid dynamics.

cs.LG

Dual-Time Smoothed Particle Hydrodynamics for Incompressible Fluid Simulation

In this paper we propose a dual-time stepping scheme for the Smoothed Particle Hydrodynamics (SPH) method. Dual-time stepping has been used in the context of other numerical methods for the simulation of incompressible fluid flows. Here we provide a scheme that combines the entropically damped artificial compressibility (EDAC) along with dual-time stepping. The method is accurate, robust, and demonstrates up to seven times better performance than the standard weakly-compressible formulation. We demonstrate several benchmarks showing the applicability of the scheme. In addition, we provide a completely open source implementation and a reproducible manuscript.

physics.comp-ph

Algorithms for uniform particle initialization in domains with complex boundaries

Accurate mesh-free simulation of fluid flows involving complex boundaries requires that the boundaries be captured accurately in terms of particles. In the context of incompressible/weakly-compressible fluid flow, the SPH method is more accurate when the particle distribution is uniform. Hence, for the time accurate simulation of flow in the presence of complex boundaries, one must have both an accurate boundary discretization as well as a uniform distribution of particles to initialize the simulation. This process of obtaining an initial uniform distribution of particles is called "particle packing". In this paper, various particle packing algorithms present in the literature are implemented and compared. An improved SPH-based algorithm is proposed which produces uniform particle distributions of both the fluid and solid domains in two and three dimensions. Some challenging geometries are constructed to demonstrate the accuracy of the new algorithm. The implementation of the algorithm is open source and the manuscript is fully reproducible.

physics.comp-ph

PySPH: a Python-based framework for smoothed particle hydrodynamics

PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is generated from this high-level Python code and executed on either multiple cores, or on GPUs, seamlessly. It also supports distributed execution using MPI. PySPH supports a wide variety of SPH schemes and formulations. These include, incompressible and compressible fluid flow, elastic dynamics, rigid body dynamics, shallow water equations, and other problems. PySPH supports a variety of boundary conditions including mirror, periodic, solid wall, and inlet/outlet boundary conditions. The package is written to facilitate reuse and reproducibility. This paper discusses the overall design of PySPH and demonstrates many of its features. Several example results are shown to demonstrate the range of features that PySPH provides.

physics.comp-ph

An efficient, open source, iterative ISPH scheme

In this paper a simple, robust, and general purpose approach to implement the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is proposed. This approach is well suited for implementation on CPUs and GPUs. The method is matrix-free and uses an iterative formulation to setup and solve the pressure-Poisson equation. A novel approach is used to ensure homogeneous particle distributions and improved boundary conditions. This formulation enables the use of solid wall boundary conditions from the weakly-compressible SPH schemes. The method is fast and runs on GPUs without the need for complex integration with sparse linear solvers. We show that this approach is sufficiently accurate and yet efficient compared to other approaches. Several benchmark problems that illustrate the robustness, performance, and wide range of applicability of the new scheme are demonstrated. An open source implementation is provided and the manuscript is fully reproducible.

math.NA