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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Further adoption of conservation tillage can increase maize yields in the western US Corn Belt

Conservation tillage can reduce soil erosion, increase soil health, and decrease labor and fuel input costs. Despite these benefits, potential yield impacts remain an important concern for farmers considering adoption. Previous research suggests that conservation tillage is likely to have the largest yield benefits in more arid conditions, but a lack of field-level analyses across climatic, management and soil conditions limits confidence in such predictions. Satellite imagery provides the opportunity to monitor agricultural lands at sub-field resolution across large spatial scales and wide environmental gradients. Here we investigate the maize yield impacts of conservation tillage in the semi-arid western US Corn Belt, using sub-field resolution datasets on tillage practices and crop yields derived from satellite data spanning four states (Nebraska, Kansas, South Dakota, and North Dakota) between 2008 and 2020. On these datasets, we estimate heterogenous yield outcomes for several thousand maize fields across gradients in climate, soil quality and irrigation status by using a causal forests analysis, an adaptation of the random forests machine-learning algorithm for causal inference on observational data. We find that long-term adoption of conservation tillage increased rainfed maize yields by an average of 9.9% in the region. Impacts on irrigated yields were small and not statistically significant. These results, along with an analysis of variables related to greater than average yield benefits, indicate that improved water infiltration and retention are the primary reasons for conservation tillage benefits. Despite yield benefits, many fields estimated to see increased yields under long term low till have not adopted the practice. Therefore, we identify specific counties likely to benefit most from increased levels of adoption. Our results strengthen the understanding of the impacts of conservation agriculture on crop yields and help define environments and counties most likely to benefit from conservation tillage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Cyber Conservative Operations

In an era of increasingly sophisticated and pervasive cyber threats, robust cyber resilience strategies are more critical than ever. This paper introduces the concept of Cyber Conservative Operations, a proactive approach designed to assist critical infrastructure owners and operators in managing risk and maintaining resilience in the face of imminent, yet not occurring, cyber events. By leveraging the principles of Cyber-Informed Engineering (CIE) and the energy sector’s practice of conservative operations, Cyber Conservative Operations offer a framework for planning and executing coordinated active defense and resilience-oriented actions ahead of cyber events. This approach aims to minimize the consequences of digitally-enabled hazards and ensure swift recovery from anticipated cyber threats. Cyber Conservative Operations enhance the ability of owners and operators to execute pre-planned defense and resilience actions, thereby reducing the impact of digitally-enabled hazards. These operations are crucial for addressing impacts that cannot be precisely quantified or forecasted and for preparing organizations for rapid recovery from imminent digital threats. The paper begins with a discussion of conservative operations as applied to the bulk power system (BPS), a current mechanism allowing BPS entities to enact defensive operating plans to mitigate impending grid unreliability. Building on this model, we present a concept for implementing cyber conservative operations at asset owner facilities. The paper concludes with two case studies of cyber conservative operations drawn from high-profile cyber events, illustrating the practical application and benefits of this proactive approach.

42 - ENGINEERING↗
DOE OSTI2022

Conformal conserved currents in embedding space

We study conformal conserved currents in arbitrary irreducible representations of the Lorentz group using the embedding space formalism. With the help of the operator product expansion, we first show that conservation conditions can be fully investigated by considering only two- and three-point correlation functions. We then find an explicitly conformally-covariant differential operator in embedding space that implements conservation based on the standard position space operator product expansion differential operator ∂μ, although the latter does not uplift to embedding space covariantly. The differential operator in embedding space that imposes conservation is the same differential operator $D_{ijA}$ used in the operator product expansion in embedding space. We provide several examples including conserved currents in irreducible representations that are not symmetric and traceless. With an eye on four-point conformal bootstrap equations for four conserved vector currents $\langle JJJJ\rangle$ and four energy-momentum tensors $\langle TTTT\rangle$, we mostly focus on conservation conditions for $\langle JJ\mathcal{O}\rangle$ and $\langle TT\mathcal{O}\rangle$. Finally, we reproduce and extend the consequences of conformal Ward identities at coincident points by determining three-point coefficients in terms of charges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite the continuous effort. Without such local conservation laws, energy and momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic fields reside on different manifolds. To overcome this difficulty, we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact, local conservation laws, in particular the energy-momentum conservation laws, for the electromagnetic gyrokinetic system. A weak Euler-Lagrange equation is established to replace the standard Euler-Lagrange equation for the particles. It is discovered that an induced weak Euler-Lagrange current enters the local conservation laws. And it is the new physics captured by the high-order field theory on heterogeneous manifolds. A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy-momentum conservation laws electromagnetic gauge-invariant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Conservation management decreases surface runoff and soil erosion

Conservation management practices – including agroforestry, cover cropping, no-till, reduced tillage, and residue return – have been applied for decades to control surface runoff and soil erosion, yet results have not been integrated and evaluated across cropping systems. In this study we collected data comparing agricultural production with and without conservation management strategies. We used a bootstrap resampling analysis to explore interactions between practice type, soil texture, surface runoff, and soil erosion. We then used a correlation analysis to relate changes in surface runoff and soil erosion to 13 other soil health and agronomic indicators, including soil organic carbon, soil aggregation, infiltration, porosity, subsurface leaching, and cash crop yield. Across all conservation management practices, surface runoff and erosion had respective mean decreases of 67% and 80% compared with controls. Use of cover cropping provided the largest decreases in erosion and surface runoff, thus emphasizing the importance of maintaining continuous vegetative cover on soils. Coarse- and medium-textured soils had greater decreases in both erosion and runoff than fine-textured soils. Changes in surface runoff and soil erosion under conservation management were highly correlated with soil organic carbon, aggregation, porosity, infiltration, leaching, and yield, showing that conservation practices help drive important interactions between these different facets of soil health. This study offers the first large-scale comparison of how different conservation agriculture practices reduce surface runoff and soil erosion, and at the same time provides new insight into how these interactions influence the improvement or loss of soil health.

58 GEOSCIENCES↗
DOE OSTI2022

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component B Ψ P of the magnetic field vector with respect to the poloidal flux function Ψ P . In an unperturbed plasma, B Ψ P can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of B Ψ P is small. In this work, we are interested in the question whether Hamiltonian conservation laws are still satisfied when B Ψ P is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without B Ψ P yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with B Ψ P retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Mass Conservation Relaxed (MCR) LSTM Model for Streamflow Simulation Across CONUS

The recent development of the physics-aware Mass-Conserving Long Short-Term Memory network (MC-LSTM) provides an alternative to other data-driven Deep Learning (DL) models in hydrology. Mass-Conserving Long Short-Term Memory incorporates mass conservation directly into the LSTM architecture. Despite the theoretical advancements, studies have reported a surprisingly limited performance of the MC-LSTM in streamflow simulation. We hypothesize that such a limitation is due to the unrealistic mass conservation scheme in MC-LSTM, which overlooks unobserved incoming water fluxes beyond precipitation. As an attempt to verify this hypothesis, we propose a Mass Conservation Relaxed LSTM (MCR-LSTM), which incorporates a bi-directional mass relaxation (MR) component to account for potential incoming water fluxes beyond precipitation. We train and test the proposed MCR-LSTM model across 531 watersheds in the contiguous United States (CONUS) against three baseline models: the Sacramento Soil Moisture Accounting, LSTM, and MC-LSTM. Our results show that MCR-LSTM outperforms MC-LSTM despite its underperformance compared to LSTM. Specifically, MCR-LSTM's advantage over MC-LSTM is mainly seen in the Plains and Western U.S., where the newly incorporated MR component better simulates water loss and suggests the likely existence of additional incoming water fluxes beyond precipitation, respectively. The novelty and contribution of this study are twofold: firstly, it introduces an alternative physics-aware DL tool (i.e., MCR-LSTM) in hydrology with higher accuracy in specific regions compared to MC-LSTM. Secondly, it provides a diagnosis of regions where strict, precipitation-based mass conservation constraints may be unrealistic in streamflow simulation.

deep learning↗
DOE OSTI2021

Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection

Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Integrating terrestrial scavenging ecology into contemporary wildlife conservation and management

Scavenging plays a vital role in maintaining ecosystem health and contributing to ecological functions; however, research in this sub-discipline of ecology is underutilized in developing and implementing wildlife conservation and management strategies. We provide an examination of the literature and recommend priorities for research where improved understanding of scavenging dynamics can facilitate the development and refinement of applied wildlife conservation and management strategies. Due to the application of scavenging research broadly within ecology, scavenging studies should be implemented for informing management decisions. In particular, a more direct link should be established between scavenging dynamics and applied management programs related to informing pharmaceutical delivery and population control through bait uptake for scavenging species, prevention of unintentional poisoning of nontarget scavenging species, the epidemiological role that scavenging species play in disease dynamics, estimating wildlife mortalities, nutrient transfer facilitated by scavenging activity, and conservation of imperiled facultative scavenging species. This commentary is intended to provide information on the paucity of data in scavenging research and present recommendations for further studies that can inform decisions in wildlife conservation and management. Additionally, we provide a framework for decision making when determining how to apply scavenging ecology research for management practices and policies. Due to the implications that scavenging species have on ecosystem health, and their overall global decline as a result of anthropic activities, it is imperative to advance studies in the field of scavenging ecology that can inform applied conservation and management programs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

An explicit, energy-conserving particle-in-cell scheme

We present an explicit temporal discretization of particle-in-cell schemes for the non-relativistic Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits $\mathcal{O}$(10 –12 ) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. Here, we also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties.

Energy conservation↗
DOE OSTI2022

Quantifying the Impact of Lagged Hydrological Responses on the Effectiveness of Groundwater Conservation

Many irrigated agricultural areas seek to prolong the lifetime of their groundwater resources by reducing pumping. However, it is unclear how lagged responses, such as reduced groundwater recharge caused by more efficient irrigation, may impact the long-term effectiveness of conservation initiatives. Here, we use a variably saturated, simplified surrogate groundwater model to: 1) analyze aquifer responses to pumping reductions, 2) quantify time lags between reductions and groundwater level responses, and 3) identify the physical controls on lagged responses. We explore a range of plausible model parameters for an area of the High Plains Aquifer (USA) where stakeholder-driven conservation has slowed groundwater depletion. We identify two types of lagged responses that reduce the long-term effectiveness of groundwater conservation, recharge-dominated and lateral-flow-dominated, with vertical hydraulic conductivity (K Z ) the major controlling variable. When high K z allows percolation to reach the aquifer, more efficient irrigation reduces groundwater recharge. By contrast, when low K z impedes vertical flow, short term changes in recharge are negligible, but pumping reductions alter the lateral flow between the groundwater conservation area and the surrounding regions (lateral-flow-dominated response). For the modeled area, we found that a pumping reduction of 30% resulted in median usable lifetime extensions of 20 or 25 years, depending on the dominant lagged response mechanism (recharge- vs. lateral-flow-dominated). These estimates are far shorter than estimates that do not account for lagged responses. To conclude, results indicate that conservation-based pumping reductions can extend aquifer lifetimes, but lagged responses can create a sizable difference between the initially perceived and actual long-term effectiveness.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Energy conservation in real-time nuclear–electronic orbital Ehrenfest dynamics

Real-time nuclear–electronic orbital Ehrenfest (RT-NEO-Ehrenfest) dynamics methods provide a first-principles approach for describing nonadiabatic molecular processes with nuclear quantum effects. For an efficient description of proton transfer within RT-NEO-Ehrenfest dynamics, the basis function center associated with the quantum proton can be allowed to move classically. Here, this traveling proton basis (TPB) approach effectively captures proton quantum dynamics, although its energy conservation behavior is not yet fully satisfactory. Two recently proposed TPB approaches, in principle, conserve the extended energy, which includes both the system energy and the kinetic energy associated with the proton basis function center. Herein, a thermostatted TPB approach is proposed to improve the conservation of the system energy, excluding the kinetic energy associated with the proton basis function center. In this approach, the quantum proton dynamics are modulated by dynamically rescaling the proton momentum operator to maintain the system energy conservation. With the excited-state intramolecular proton transfer of o-hydroxybenzaldehyde as an example, this approach is shown to significantly improve the system energy conservation while preserving the accuracy of the quantum proton dynamics as achieved in the original TPB approach.

Ehrenfest dynamics↗
DOE OSTI2024

One hundred priority questions for advancing seagrass conservation in Europe

Societal Impact Statement Seagrass ecosystems are of fundamental importance to our planet and wellbeing. Seagrasses are marine flowering plants, which engineer ecosystems that provide a multitude of ecosystem services, for example, blue foods and carbon sequestration. Seagrass ecosystems have largely been degraded across much of their global range. There is now increasing interest in the conservation and restoration of these systems, particularly in the context of the climate emergency and the biodiversity crisis. The collation of 100 questions from experts across Europe could, if answered, improve our ability to conserve and restore these systems by facilitating a fundamental shift in the success of such work. Summary Seagrass meadows provide numerous ecosystem services including biodiversity, coastal protection, and carbon sequestration. In Europe, seagrasses can be found in shallow sheltered waters along coastlines, in estuaries & lagoons, and around islands, but their distribution has declined. Factors such as poor water quality, coastal modification, mechanical damage, overfishing, land‐sea interactions, climate change and disease have reduced the coverage of Europe’s seagrasses necessitating their recovery. Research, monitoring and conservation efforts on seagrass ecosystems in Europe are mostly uncoordinated and biased towards certain species and regions, resulting in inadequate delivery of critical information for their management. Here, we aim to identify the 100 priority questions, that if addressed would strongly advance seagrass monitoring, research and conservation in Europe. Using a Delphi method, researchers, practitioners, and policymakers with seagrass experience from across Europe and with diverse seagrass expertise participated in the process that involved the formulation of research questions, a voting process and an online workshop to identify the final list of the 100 questions. The final list of questions covers areas across nine themes: Biodiversity & Ecology; Ecosystem services; Blue carbon; Fishery support; Drivers, Threats, Resilience & Response; Monitoring & Assessment; Conservation & Restoration; Governance, Policy & Management; and Communication. Answering these questions will fill current knowledge gaps and place European seagrass onto a positive trajectory of recovery.

Nordlund, Lina Mtwana↗
DOE OSTI2023

Ecologically-Informed Precision Conservation: A framework for increasing biodiversity in intensively managed agricultural landscapes with minimal sacrifice in crop production

Conservation actions are urgently needed to tackle biodiversity loss in intensively managed agricultural landscapes. Production lands are usually heterogeneous and contain low-yield areas that can be set aside for biodiversity conservation without serious yield losses. Here, we introduce Ecologically-Informed Precision Conservation, a framework that integrates yield mapping and ecological theory to select the best areas to create new set-asides while ensuring high crop yields at the farm/landscape level. Long-term yield maps can be generated using globally available satellite data and basic information on field/farm crop yield from farmers. Ecological principles are then used to select the subset of areas with the highest potential for biodiversity conservation by prioritising those that increase connectivity, maximise habitat heterogeneity and decrease landscape grain size. Here, the created non-crop habitats can be permanent and thus ensure biodiversity support over time. In addition, agricultural management efficiency can be enhanced by improving field shapes. The framework provides the basis for a practical, user-friendly tool that informs all interested stakeholders on how to rationalise existing agricultural landscapes using already-existing farming systems and available technologies. High cost-effectiveness from an economic and conservation perspective, along with the creation of heterogeneous non-crop habitats, make our framework a promising solution to re-design agricultural landscapes.

Precision agriculture↗
DOE OSTI2022

A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

We report that the hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical m = 1 mode simulation for magnetic fusion energy application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Immunogenicity and protective efficacy of a rhesus adenoviral vaccine targeting conserved COVID-19 replication transcription complex

The COVID-19 pandemic marks the third coronavirus pandemic this century (SARS-CoV-1, MERS, SARS-CoV-2), emphasizing the need to identify and evaluate conserved immunogens for a pan-sarbecovirus vaccine. Here we investigate the potential utility of a T-cell vaccine strategy targeting conserved regions of the sarbecovirus proteome. We identified the most conserved regions of the sarbecovirus proteome as portions of the RNA-dependent RNA polymerase (RdRp) and Helicase proteins, both of which are part of the coronavirus replication transcription complex (RTC). Fitness constraints suggest that as SARS-CoV-2 continues to evolve these regions may better preserve cross-reactive potential of T-cell responses than Spike, Nucleocapsid, or Membrane proteins. We sought to determine if vaccine-elicited T-cell responses to the highly conserved regions of the RTC would reduce viral loads following challenge with SARS-CoV-2 in mice using a rhesus adenovirus serotype 52 (RhAd52) vector. The RhAd52.CoV.Consv vaccine generated robust cellular immunity in mice and led to significant reductions in viral loads in the nasal turbinates following challenge with a mouse-adapted SARS-CoV-2. These data suggest the potential utility of T-cell targeting of conserved regions for a pan-sarbecovirus vaccine.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Accuracy of the explicit energy-conserving particle-in-cell method for under-resolved simulations of capacitively coupled plasma discharges

The traditional explicit electrostatic momentum-conserving particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical stability and accuracy. The explicit electrostatic energy-conserving particle-in-cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity, ease of parallelization, and acceleration on modern supercomputing architectures. In this article, we apply the algorithm to model a one-dimensional radio frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8 times the electron Debye length. For even larger cells, the algorithm loses accuracy due to poor resolution of steep gradients within the radio frequency sheath. Accuracy can be recovered by adopting a non-uniform grid, which resolves the sheath and allows for cell sizes up to 32 times the electron Debye length in the quasi-neutral bulk of the discharge. The effect is an up to 8 times reduction in the number of required simulation cells, an improvement that can compound in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Energy conserving and well-balanced discontinuous Galerkin methods for the Euler–Poisson equations in spherical symmetry

ABSTRACT This paper presents high-order Runge–Kutta (RK) discontinuous Galerkin methods for the Euler–Poisson equations in spherical symmetry. The scheme can preserve a general polytropic equilibrium state and achieve total energy conservation up to machine precision with carefully designed spatial and temporal discretizations. To achieve the well-balanced property, the numerical solutions are decomposed into equilibrium and fluctuation components that are treated differently in the source term approximation. One non-trivial challenge encountered in the procedure is the complexity of the equilibrium state, which is governed by the Lane–Emden equation. For total energy conservation, we present second- and third-order RK time discretization, where different source term approximations are introduced in each stage of the RK method to ensure the conservation of total energy. A carefully designed slope limiter for spherical symmetry is also introduced to eliminate oscillations near discontinuities while maintaining the well-balanced and total-energy-conserving properties. Extensive numerical examples – including a toy model of stellar core collapse with a phenomenological equation of state that results in core bounce and shock formation – are provided to demonstrate the desired properties of the proposed methods, including the well-balanced property, high-order accuracy, shock-capturing capability, and total energy conservation.

79 ASTRONOMY AND ASTROPHYSICS↗