arXiv subjects

Amareshwara Sainadh Chamarthi

Publications and source records attributed to Amareshwara Sainadh Chamarthi.

At least 19 recordsLinked to original sources

arXiv2026

Wave-Appropriate Reconstruction of Compressible Multiphase and Multicomponent Flows: Fully Conservative and Semi-Conservative Eigenstructures

Compressible multiphase and multicomponent solvers require accurate interface representation without spurious pressure oscillations. At material interfaces, pressure and velocity are continuous while density and the equation of state exhibit abrupt discontinuities. Standard approaches reconstruct primitive or characteristic variables to capture these properties, but do not clarify the failure mechanisms of conservative reconstruction or fully leverage the wave-decoupling advantages of characteristic decomposition. This work derives the complete eigenstructure of the Allaire five-equation model for two variable sets. In the fully conservative~(FC) formulation, $\mathbf{U} = [α_1ρ_1,\,α_2ρ_2,\,ρu,\,ρv,\,ρE,\,α_1]^T$, eigenvectors contain a thermodynamic jump term~$Ψ$ that enforces $dp=0$ and $du=0$ at material contacts by compensating for compressibility mismatches. In the semi-conservative~(SC) formulation, $\mathbf{V} = [α_1ρ_1,\,α_2ρ_2,\,ρu,\,ρv,\,p,\,α_1]^T$, the volume-fraction eigenvector carries a structural zero in the pressure slot, enforcing equilibrium without thermodynamic correction. Explicit left and right eigenvectors are derived for one- and two-dimensional stiffened-gas flows. Both formulations satisfy Abgrall's equilibrium condition when reconstruction is performed in characteristic space; reconstruction in physical space yields $\mathcal{O}(1)$ pressure and velocity errors at interfaces regardless of the variable set. The eigenvector structure further reveals that the shear wave is decoupled from all thermodynamic and interface fields in both formulations, extending this result from single-species to compressible multiphase flows including gas-liquid configurations. One- and two-dimensional gas-gas and gas-liquid test cases confirm oscillation-free, accurate results.

physics.flu-dyn↗

arXiv2026

Wave-appropriate reconstruction of compressible flows: physics-constrained acoustic dissipation and rank-1 entropy wave correction

The wave-appropriate reconstruction approach decomposes the reconstruction procedure into characteristic wave families, centralizing non-acoustic waves to minimize dissipation while retaining an upwind bias for acoustic waves. In previous implementations, the acoustic upwind parameter $η_a$ was fixed at its maximum value of $1.0$; however, this choice is conservative and motivated a systematic search for the minimum value that is robust across flow regimes. To this end, the CFD solver is treated as a black box within a bounded scalar minimization, which minimizes an accuracy objective for the subsonic inviscid TGV subject to a stability constraint enforced by the supersonic viscous TGV. Because the wave-appropriate framework leaves $η_a$ as the sole degree of freedom, the optimization converges in approximately 25 evaluations. The resulting optimal values generalize without retuning across a wide range from subsonic turbulence to hypersonic flows with shocks and contact discontinuities. The second contribution focuses on eliminating the need for an explicit contact-discontinuity detector, which is commonly required in flows involving both shock waves and contact discontinuities. In such cases, the reconstruction deficiency appears solely within the entropy characteristic wave and can be corrected by a rank-1 update along the entropy right eigenvector. The proposed algorithm relies only on the Ducros sensor and is limiter-agnostic, facilitating direct use in other schemes, such as WENO. This approach reduces wall time by $29$--$41\%$ compared to full characteristic decomposition. To further demonstrate the method's generality, introducing a controlled acoustic bias exclusively to the normal momentum in a KEP scheme eliminates spurious vortices in periodic shear layers, confirming that the acoustic stability mechanism operates independently of the discretization framework.

physics.flu-dyn↗

arXiv2026

Acoustic Loading Beneath High-Speed Flow Over a Compression Ramp at Different Angles

Large-eddy simulations are performed to characterize the pressure fluctuations beneath a hypersonic boundary layer approaching a compression corner. The simulations are carried out at Mach 6.04 and an inlet momentum-thickness Reynolds number of $Re_θ=4340$. The compression-corner angle is varied over $10^\circ$, $20^\circ$, $30^\circ$, and $34^\circ$ spanning attached to strongly separated regimes. The peak root-mean-square wall-pressure fluctuations intensity increases sharply with separation strength, rising by $312\%$ from R20 to R30 and a further $67\%$ from R30 to R34, with the peak located downstream of reattachment. Notably, acoustic loading increases from 140 dB in the approach flow to $\approx177$ dB downstream of reattachment in the $34^\circ$ case. Further analysis reveals that intense intermittent pressure events are concentrated near the shock foot, spatially distinct from the peak acoustic-loading region, where fluctuations are relatively sustained. With increasing interaction strength, spectral energy shifts from turbulence-dominated high frequencies to broadband low-frequency motion. Band-isolated acoustic loading maps reveal high-frequency fluctuations as the dominant contributor across the interaction zone, with low-frequency fluctuations becoming locally comparable in the R34 case near the separation region. Spatio-temporal maps of bandpass-filtered pressure fluctuations reveal downstream convecting Kelvin-Helmholtz structures and upstream propagating pressure waves near the shock foot.

physics.flu-dyn↗

arXiv2026

On Reconstructing Conservative and Primitive Variables: An Eigenvector Analysis on Curvilinear Grids

In wall-modelled large-eddy simulations of hypersonic boundary-layer transition, Hoffmann, Chamarthi and Frankel reported that characteristic reconstruction based on conservative-variable eigenvectors produced markedly better results than the corresponding primitive-variable implementation. The observation was empirical. A subsequent wave-appropriate conservative reconstruction (WA-CR) algorithm used a rank-one entropy correction based on the premise that contact-discontinuity error lies in a single conservative entropy/contact direction. This note gives the algebraic foundation for both observations. For the standard conservative curvilinear eigenvectors, the density row of the right-eigenvector matrix contains exact, metric-free zeros in the shear columns, so shear waves carry no density perturbation and a contact discontinuity is represented by the conservative entropy eigenvector alone. The conservative left eigenvectors provide the dual projection property: the entropy amplitude is obtained with a metric-independent left eigenvector and has unit contact scaling, while total-energy perturbations have zero projection onto the shear amplitudes. In the standard primitive curvilinear eigenvectors, by contrast, shear right eigenvectors contain metric-dependent density components and the primitive entropy left eigenvector contains metric-weighted tangential-velocity terms. Thus the conservative formulation supplies the two algebraic requirements for an exact, sufficient, metric-invariant, rank-one entropy correction: metric-independent entropy projection and a metric-independent entropy update direction. Curvilinear metrics make the distinction explicit, but the conservative state-space contact direction is already the natural direction underlying WA-CR even on Cartesian grids.

physics.comp-ph↗

arXiv2025

Consistent Interface Capturing Adaptive Reconstruction Approach for Viscous Compressible Multicomponent Flows

The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate variables (phasic densities). For other flow regions, the variables are reconstructed using the Monotonicity-preserving (MP) scheme (or Weighted essentially non-oscillatory scheme (WENO)). For reconstruction in the characteristic space, the THINC approach is used only for the contact (or entropy) wave and volume fractions and for the reconstruction of primitive variables, the THINC approach is used for phasic densities and volume fractions only, offering an effective solution for reducing dissipation errors near contact discontinuities. The second contribution is the development of an algorithm that uses a central reconstruction scheme for the tangential velocities, as they are continuous across material interfaces in viscous flows. In this regard, the Ducros sensor (a shock detector that cannot detect material interfaces) is employed to compute the tangential velocities using a central scheme across material interfaces. Using the central scheme does not produce any oscillations at the material interface. The proposed approach is thoroughly validated with several benchmark test cases for compressible multicomponent flows, highlighting its advantages. The numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods.

physics.flu-dyn↗

arXiv2025

Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows

This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In characteristic space, upwind schemes are used for acoustic waves, central schemes for vorticity and entropy waves, and Tangent of Hyper-bola for INterface Capturing (THINC) reconstruction for material interfaces and contact discontinuities (a subset of entropy waves). This approach prevents spurious vortices in periodic shear layers, accurately captures vortical structures in gas-gas and gas-liquid interactions, and improves the accuracy of shock-entropy wave interactions. In physical space, phasic densities are computed using THINC in regions of contact discontinuities and material interfaces, while tangential velocities are calculated with central schemes to improve vortical structures. An adaptive reconstruction technique is also introduced to mitigate oscillations near shocks, which arise from primitive variable reconstruction, by combining primitive and characteristic variable reconstructions with the liquid phase being identified using the stiffened gas parameter. The proposed multidimensional upwinding approach outperforms traditional schemes, demonstrating superior accuracy in capturing physical phenomena, reducing numerical artifacts, and better matching experimental results across complex test cases.

physics.flu-dyn↗

arXiv2024

A generalized adaptive central-upwind scheme for compressible flow simulations and preventing spurious vortices

This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the central gradient-based reconstruction approach presented in [1] (Hoffmann, Chamarthi and Frankel, JCP 2024). By leveraging a combination of conservative and characteristic variable reconstruction, the proposed approach demonstrates oscillation-free results while effectively reducing computational costs and improving the results. Furthermore, the adaptive central-upwind algorithm is generalized to be compatible not only with the gradient-based reconstruction as in [1] but with other existing methods. In this regard, with the proposed algorithm, the standard fifth/sixth-order reconstruction scheme has also been shown to outperform existing schemes with a 20-30% reduction in computational expense with improved results. Notably, the proposed approach has successfully prevented the generation of spurious vortices in the double shear layer test cases, even with linear schemes, showcasing its robustness and effectiveness.

physics.flu-dyn↗

arXiv2024

Centralized Gradient-Based Reconstruction for Wall Modelled Large Eddy Simulations of Hypersonic Boundary Layer Transition

In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which require upwinding for stability. Distinct differences were observed between transformations using either primitive or conservative variables. We evaluated the method's robustness and superiority using benchmark problems, including the two-dimensional shock entropy problem, two-dimensional viscous shock tube, and three-dimensional inviscid Taylor-Green vortex. Subsequently, we assessed the method in the context of Wall Modelled Large Eddy Simulations (WMLES), where coarse grids are used to reduce computational cost but also introduce substantial numerical dissipation. Using WMLES, we simulated oblique shock impingement on a Mach 6 disturbed boundary layer and a Mach 7.7 flow over a $15^{\circ}$ compression ramp. Our findings reveal that: 1) transformation to characteristic space using conservative variables leads to more accurate results; 2) minimizing numerical dissipation through centralized interpolation is crucial. In the compression ramp case, boundary layer separation was shifted slightly upstream, and there was an over-prediction of wall heating, likely attributable to the equilibrium-assuming wall model. Overall, this work showcases the method's potential in accurately capturing complex flow dynamics with reduced numerical dissipation.

physics.flu-dyn↗

arXiv2023

A Wave Appropriate Discontinuity Sensor Approach for Compressible Flows

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the Gradient-Based Reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor-Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow.

physics.flu-dyn↗

arXiv2023

Efficient high-order Gradient-based Reconstruction for compressible flows

This paper extends the gradient-based reconstruction approach of Chamarthi \cite{chamarthi2023gradient} to genuine high-order accuracy for inviscid test cases involving smooth flows. A seventh-order accurate scheme is derived using the same stencil as of the explicit fourth-order scheme proposed in Ref. \cite{chamarthi2023gradient}, which also has low dissipation properties. The proposed method is seventh-order accurate under the assumption that the variables at the \textit{cell centres are point values}. A problem-independent discontinuity detector is used to obtain high-order accuracy. Accordingly, primitive or conservative variable reconstruction is performed around regions of discontinuities, whereas smooth solution regions apply flux reconstruction. The proposed approach can still share the derivatives between the inviscid and viscous fluxes, which is the main idea behind the gradient-based reconstruction. Several standard benchmark test cases are presented. The proposed method is more efficient than the seventh-order weighted compact nonlinear scheme (WCNS) for the test cases considered in this paper.

physics.flu-dyn↗

arXiv2023

On the Application of Gradient Based Reconstruction for Flow Simulations on Generalized Curvilinear and Dynamic Mesh Domains

Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and $α$-damping schemes introduced by Chamarthi (2022) [1] for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test cases. It has been shown both theoretically and through the use of test cases that the conservative metrics, including their interpolation to cell interfaces, must be numerically computed using a central scheme that is consistent with the inviscid flux algorithm to achieve the freestream preservation property. The second part of the paper illustrates the efficacy of the algorithm in simulating supersonic jet screech by displaying its capability to capture the screech tones and accurately characterize the unsteady lateral flapping mode of a Mach 1.35 under-expanded supersonic jet, in contrast to the WENO-Z scheme which fails to do so at the same grid resolution. In the final part of the paper, the parallelizability of the schemes on GPU architectures is demonstrated and performance metrics are evaluated. A significant speedup of over $200 \times$ (compared to a single core CPU) and a reduction in simulation completion time to 34.5 hours per simulation were achieved for the supersonic jet noise case at a grid resolution of 13 million cells.

physics.flu-dyn↗

arXiv2023

Implicit gradients based conservative numerical scheme for compressible flows

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed method's capability using the implicit gradient method for compressible flows.

math.NA↗

arXiv2022

On the role of spectral properties of viscous flux discretization for flow simulations on marginally resolved grids

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with better properties at high wavenumbers, denoted as $α$-damping type discretization, produced superior solutions compared to the other class of methods. The proposed compact $α$-damping method converged towards the direct numerical simulation (DNS) solution at lower grid resolution compared with the other class of methods and is, therefore, a better candidate for high fidelity large-eddy simulations (LES) and DNS studies.

physics.flu-dyn↗

arXiv2022

Gradient Based Reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of derivatives. The higher-order accurate gradients of the velocity components are reused to compute the viscous fluxes for efficiency and significantly improve the solution and gradient quality, as demonstrated by several viscous-flow test cases. The viscous schemes are fourth-order accurate and carefully designed with a high-frequency damping property, which has been identified as a critically important property for stable compressible-flow simulations with shock waves [Chamarthi et al., JCP, 2022]. Shocks and material discontinuities are captured using a monotonicity-preserving (MP) scheme, which is also improved by reusing the gradients. For inviscid test cases, The proposed scheme is fourth-order for linear and second-order accurate for non-linear problems. Several numerical results obtained for simulations of complex viscous flows are presented to demonstrate the accuracy and robustness of the proposed methodology.

physics.flu-dyn↗

arXiv2022

On the Importance of High-Frequency Damping in High-Order Conservative Finite-Difference Schemes for Viscous Fluxes

This paper discusses the importance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Investigating nonlinear instability encountered in a high-resolution viscous shock-tube simulation, we have discovered that a modification to the viscous scheme rather than the inviscid scheme resolves a problem with spurious oscillations around shocks. The modification introduces a term responsible for high-frequency damping that is missing in a conservative high-order viscous scheme. The importance of damping has been known for schemes designed for unstructured grids. However, it has not been recognized well in very high-order difference schemes, especially in conservative difference schemes. Here, we discuss how it is easily missed in a conservative scheme and how to improve such schemes by a suitably designed damping term.

math.NA↗

arXiv2021

Implicit gradients based novel finite volume scheme for compressible single and multi-component flows

This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. The new finite volume scheme has superior dispersion and dissipation properties in comparison to the compact reconstruction approach. These implicit gradients are re-used in viscous flux computation and post-processing, which further improves efficiency. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed finite volume method's capability using the implicit gradient method for single and multicomponent flows. Significant improvements are observed by computing the gradients implicitly for the viscous flows.

math.NA↗

arXiv2020

High-Order Central-Upwind shock capturing scheme using a Boundary Variation Diminishing (BVD) Algorithm

In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.

math.NA↗

arXiv2019

First order hyperbolic approach for Anisotropic Diffusion equation

In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order scheme that is independent of the degree of anisotropy is made straightforward by the hyperbolic method with an optimal length scale. We demonstrate that the gradients are computed simultaneously to the same order of accuracy as that of the solution variable by using weight compact finite difference schemes. Furthermore, the approach is extended to improve further the simulation of the magnetized electrons test case previously discussed in Refs.[J. Comput. Phys., 284 (2015) 59-69 and 374 (2018) 1120-1151]. Numerical results indicate that these schemes are capable of delivering high accuracy and the proposed approach is expected to allow the hyperbolic method to be successfully applied to a wide variety of linear and nonlinear problems with anisotropic diffusion.

physics.comp-ph↗