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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 703 records · Page 39
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DOE OSTI2015

Treatment Guidelines for Preoperative Radiation Therapy for Retroperitoneal Sarcoma: Preliminary Consensus of an International Expert Panel

Purpose: Evidence for external beam radiation therapy (RT) as part of treatment for retroperitoneal sarcoma (RPS) is limited. Preoperative RT is the subject of a current randomized trial, but the results will not be available for many years. In the meantime, many practitioners use preoperative RT for RPS, and although this approach is used in practice, there are no radiation treatment guidelines. An international expert panel was convened to develop consensus treatment guidelines for preoperative RT for RPS. Methods and Materials: An expert panel of 15 academic radiation oncologists who specialize in the treatment of sarcoma was assembled. A systematic review of reports related to RT for RPS, RT for extremity sarcoma, and RT-related toxicities for organs at risk was performed. Due to the paucity of high-quality published data on the subject of RT for RPS, consensus recommendations were based largely on expert opinion derived from clinical experience and extrapolation of relevant published reports. It is intended that these clinical practice guidelines be updated as pertinent data become available. Results: Treatment guidelines for preoperative RT for RPS are presented. Conclusions: An international panel of radiation oncologists who specialize in sarcoma reached consensus guidelines for preoperative RT for RPS. Many of the recommendations are based on expert opinion because of the absence of higher level evidence and, thus, are best regarded as preliminary. We emphasize that the role of preoperative RT for RPS has not been proven, and we await data from the European Organization for Research and Treatment of Cancer (EORTC) study of preoperative radiotherapy plus surgery versus surgery alone for patients with RPS. Further data are also anticipated pertaining to normal tissue dose constraints, particularly for bowel tolerance. Nonetheless, as we await these data, the guidelines herein can be used to establish treatment uniformity to aid future assessments of efficacy and toxicity.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Outcomes for Spine Stereotactic Body Radiation Therapy and an Analysis of Predictors of Local Recurrence

Purpose: To investigate local control, survival outcomes, and predictors of local relapse for patients treated with spine stereotactic body radiation therapy. Methods and Materials: We reviewed the records of 332 spinal metastases consecutively treated with stereotactic body radiation therapy between 2002 and 2012. The median follow-up for all living patients was 33 months (range, 0-111 months). Endpoints were overall survival and local control (LC); recurrences were classified as either in-field or marginal. Results: The 1-year actuarial LC and overall survival rates were 88% and 64%, respectively. Patients with local relapses had poorer dosimetric coverage of the gross tumor volume (GTV) compared with patients without recurrence (minimum dose [Dmin] biologically equivalent dose [BED] 23.9 vs 35.1 Gy, P<.001; D98 BED 41.8 vs 48.1 Gy, P=.001; D95 BED 47.2 vs 50.5 Gy, P=.004). Furthermore, patients with marginal recurrences had poorer prescription coverage of the GTV (86% vs 93%, P=.01) compared with those with in-field recurrences, potentially because of more upfront spinal canal disease (78% vs 24%, P=.001). Using a Cox regression univariate analysis, patients with a GTV BED Dmin ≥33.4 Gy (median dose) (equivalent to 14 Gy in 1 fraction) had a significantly higher 1-year LC rate (94% vs 80%, P=.001) compared with patients with a lower GTV BED Dmin; this factor was the only significant variable on multivariate Cox analysis associated with LC (P=.001, hazard ratio 0.29, 95% confidence interval 0.14-0.60) and also was the only variable significant in a separate competing risk multivariate model (P=.001, hazard ratio 0.30, 95% confidence interval 0.15-0.62). Conclusions: Stereotactic body radiation therapy offers durable control for spinal metastases, but there is a subset of patients that recur locally. Patients with local relapse had significantly poorer tumor coverage, which was likely attributable to treatment planning directives that prioritized the spinal cord constraints over tumor coverage. When possible, we recommend maintaining a GTV Dmin above 14 Gy in 1 fraction and 21 Gy in 3 fractions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Trajectory Modulated Arc Therapy: A Fully Dynamic Delivery With Synchronized Couch and Gantry Motion Significantly Improves Dosimetric Indices Correlated With Poor Cosmesis in Accelerated Partial Breast Irradiation

Purpose: To develop planning and delivery capabilities for linear accelerator–based nonisocentric trajectory modulated arc therapy (TMAT) and to evaluate the benefit of TMAT for accelerated partial breast irradiation (APBI) with the patient in prone position. Methods and Materials: An optimization algorithm for volumetrically modulated arc therapy (VMAT) was generalized to allow for user-defined nonisocentric TMAT trajectories combining couch rotations and translations. After optimization, XML scripts were automatically generated to program and subsequently deliver the TMAT plans. For 10 breast patients in the prone position, TMAT and 6-field noncoplanar intensity modulated radiation therapy (IMRT) plans were generated under equivalent objectives and constraints. These plans were compared with regard to whole breast tissue volume receiving more than 100%, 80%, 50%, and 20% of the prescription dose. Results: For TMAT APBI, nonisocentric collision-free horizontal arcs with large angular span (251.5 ± 7.9°) were optimized and delivered with delivery time of ∼4.5 minutes. Percentage changes of whole breast tissue volume receiving more than 100%, 80%, 50%, and 20% of the prescription dose for TMAT relative to IMRT were −10.81% ± 6.91%, −27.81% ± 7.39%, −14.82% ± 9.67%, and 39.40% ± 10.53% (P≤.01). Conclusions: This is a first demonstration of end-to-end planning and delivery implementation of a fully dynamic APBI TMAT. Compared with IMRT, TMAT resulted in marked reduction of the breast tissue volume irradiated at high doses.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Impact of Fractionation and Dose in a Multivariate Model for Radiation-Induced Chest Wall Pain

Purpose: To determine the role of patient/tumor characteristics, radiation dose, and fractionation using the linear-quadratic (LQ) model to predict stereotactic body radiation therapy–induced grade ≥2 chest wall pain (CWP2) in a larger series and develop clinically useful constraints for patients treated with different fraction numbers. Methods and Materials: A total of 316 lung tumors in 295 patients were treated with stereotactic body radiation therapy in 3 to 5 fractions to 39 to 60 Gy. Absolute dose–absolute volume chest wall (CW) histograms were acquired. The raw dose-volume histograms (α/β = ∞ Gy) were converted via the LQ model to equivalent doses in 2-Gy fractions (normalized total dose, NTD) with α/β from 0 to 25 Gy in 0.1-Gy steps. The Cox proportional hazards (CPH) model was used in univariate and multivariate models to identify and assess CWP2 exposed to a given physical and NTD. Results: The median follow-up was 15.4 months, and the median time to development of CWP2 was 7.4 months. On a univariate CPH model, prescription dose, prescription dose per fraction, number of fractions, D83cc, distance of tumor to CW, and body mass index were all statistically significant for the development of CWP2. Linear-quadratic correction improved the CPH model significance over the physical dose. The best-fit α/β was 2.1 Gy, and the physical dose (α/β = ∞ Gy) was outside the upper 95% confidence limit. With α/β = 2.1 Gy, V{sub NTD99Gy} was most significant, with median V{sub NTD99Gy} = 31.5 cm{sup 3} (hazard ratio 3.87, P<.001). Conclusion: There were several predictive factors for the development of CWP2. The LQ-adjusted doses using the best-fit α/β = 2.1 Gy is a better predictor of CWP2 than the physical dose. To aid dosimetrists, we have calculated the physical dose equivalent corresponding to V{sub NTD99Gy} = 31.5 cm{sup 3} for the 3- to 5-fraction groups.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Evaluation of the Risk of Grade 3 Oral and Pharyngeal Dysphagia Using Atlas-Based Method and Multivariate Analyses of Individual Patient Dose Distributions

Purpose: The study aimed to apply the atlas of complication incidence (ACI) method to patients receiving radical treatment for head and neck squamous cell carcinomas (HNSCC), to generate constraints based on dose-volume histograms (DVHs), and to identify clinical and dosimetric parameters that predict the risk of grade 3 oral mucositis (g3OM) and pharyngeal dysphagia (g3PD). Methods and Materials: Oral and pharyngeal mucosal DVHs were generated for 253 patients who received radiation (RT) or chemoradiation (CRT). They were used to produce ACI for g3OM and g3PD. Multivariate analysis (MVA) of the effect of dosimetry, clinical, and patient-related variables was performed using logistic regression and bootstrapping. Receiver operating curve (ROC) analysis was also performed, and the Youden index was used to find volume constraints that discriminated between volumes that predicted for toxicity. Results: We derived statistically significant dose-volume constraints for g3OM over the range v28 to v70. Only 3 statistically significant constraints were derived for g3PD v67, v68, and v69. On MVA, mean dose to the oral mucosa predicted for g3OM and concomitant chemotherapy and mean dose to the inferior constrictor (IC) predicted for g3PD. Conclusions: We have used the ACI method to evaluate incidences of g3OM and g3PD and ROC analysis to generate constraints to predict g3OM and g3PD derived from entire individual patient DVHs. On MVA, the strongest predictors were radiation dose (for g3OM) and concomitant chemotherapy (for g3PD).

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Stereotactic Body Radiation Therapy Boost After Concurrent Chemoradiation for Locally Advanced Non-Small Cell Lung Cancer: A Phase 1 Dose Escalation Study

Purpose: Stereotactic body radiation therapy (SBRT) boost to primary and nodal disease after chemoradiation has potential to improve outcomes for advanced non-small cell lung cancer (NSCLC). A dose escalation study was initiated to evaluate the maximum tolerated dose (MTD). Methods and Materials: Eligible patients received chemoradiation to a dose of 50.4 Gy in 28 fractions and had primary and nodal volumes appropriate for SBRT boost (<120 cc and <60 cc, respectively). SBRT was delivered in 2 fractions after chemoradiation. Dose was escalated from 16 to 28 Gy in 2 Gy/fraction increments, resulting in 4 dose cohorts. MTD was defined when ≥2 of 6 patients per cohort experienced any treatment-related grade 3 to 5 toxicity within 4 weeks of treatment or the maximum dose was reached. Late toxicity, disease control, and survival were also evaluated. Results: Twelve patients (3 per dose level) underwent treatment. All treatment plans met predetermined dose-volume constraints. The mean age was 64 years. Most patients had stage III disease (92%) and were medically inoperable (92%). The maximum dose level was reached with no grade 3 to 5 acute toxicities. At a median follow-up time of 16 months, 1-year local-regional control (LRC) was 78%. LRC was 50% at <24 Gy and 100% at ≥24 Gy (P=.02). Overall survival at 1 year was 67%. Late toxicity (grade 3-5) was seen in only 1 patient who experienced fatal bronchopulmonary hemorrhage (grade 5). There were no predetermined dose constraints for the proximal bronchial-vascular tree (PBV) in this study. This patient's 4-cc PBV dose was substantially higher than that received by other patients in all 4 cohorts and was associated with the toxicity observed: 20.3 Gy (P<.05) and 73.5 Gy (P=.07) for SBRT boost and total treatment, respectively. Conclusions: SBRT boost to both primary and nodal disease after chemoradiation is feasible and well tolerated. Local control rates are encouraging, especially at doses ≥24 Gy in 2 fractions. Toxicity at the PBV is a concern but potentially can be avoided with strict dose-volume constraints.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Conformal Avoidance of Normal Organs at Risk by Perfusion-Modulated Dose Sculpting in Tumor Single-Dose Radiation Therapy

Although 24 Gy single-dose radiation therapy (SDRT) renders >90% 5-year local relapse-free survival in human solid tumor lesions, SDRT delivery is not feasible in ∼50% of oligometastatic lesions owing to interference by dose/volume constraints of a serial organ at risk (OAR). Conformal OAR avoidance is based on a hypothetical model positing that the recently described SDRT biology specifically permits volumetric subdivision of the SDRT dose, such that high-intensity vascular drivers of SDRT lethality, generated within a major tumor subvolume exposed to a high 24 Gy dose (high-dose planning target volume [PTV{sub HD]}), would equilibrate SDRT signaling intensity throughout the tumor interstitial space, rendering bystander radiosensitization of a minor subvolume (perfusion-modulated dose sculpting PTV [PTV{sub PMDS}]), dose-sculpted to meet a serial OAR dose/volume constraint. An engineered PTV{sub PMDS} may thus yield tumor ablation despite PMDS dose reduction and conformally avoiding OAR exposure to a toxic dose.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Use of Multi-Site Radiation Therapy for Systemic Disease Control

Metastatic cancer is a heterogeneous entity, some of which could benefit from local consolidative radiation therapy (RT). Although randomized evidence is growing in support of using RT for oligometastatic disease, a highly active area of investigation relates to whether RT could benefit patients with polymetastatic disease. This article highlights the preclinical and clinical rationale for using RT for polymetastatic disease, proposes an exploratory framework for selecting patients best suited for these types of treatments, and briefly reviews potential challenges. The goal of this hypothesis-generating review is to address personalized multimodality systemic treatment for patients with metastatic cancer. The rationale for using high-dose RT is primarily for local control and immune activation in either oligometastatic or polymetastatic disease. However, the primary application of low-dose RT is to activate distinct antitumor immune pathways and modulate the tumor stroma in efforts to better facilitate T cell infiltration. We explore clinical cases involving high- and low-dose RT to demonstrate the potential efficacy of such treatment. We then group patients by extent of disease burden to implement high- and/or low-dose RT. Patients with low-volume disease may receive high-dose RT to all sites as part of an oligometastatic paradigm. Subjects with high-volume disease (for whom standard of care remains palliative RT only) could be treated with a combination of high-dose RT to a few sites for immune activation, while receiving low-dose RT to several remaining lesions to enhance systemic responses from high-dose RT and immunotherapy. We further discuss how emerging but speculative concepts such as immune function may be integrated into this approach and examine therapies currently under investigation that may help address immune deficiencies. The review concludes by addressing challenges in using RT for polymetastatic disease, such as concerns about treatment planning workflows, treatment times, dose constraints for multiple-isocenter treatments, and economic considerations.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Safety Margins for the Delineation of the Left Anterior Descending Artery in Patients Treated for Breast Cancer

Cardiac toxicity after breast cancer (BC) radiation therapy is partly due to the large radiation doses to coronary arteries. The left anterior descending artery (LAD) is particularly exposed. A first step in achieving robust dose constraints to the LAD during treatment planning is homogeneous delineation based on guidelines. LAD delineation can be problematic due to heart movements. The aim of the study was to establish a safety margin for delineation of the LAD in patients with BC.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Modern Radiation Therapy for Extranodal Nasal-Type NK/T-cell Lymphoma: Risk-Adapted Therapy, Target Volume, and Dose Guidelines from the International Lymphoma Radiation Oncology Group

In the multidisciplinary management of early-stage extranodal natural killer/T-cell lymphoma, nasal type (ENKTCL), with curative intent, radiation therapy is the most efficacious modality and is an essential component of a combined-modality regimen. In the past decade, utilization of upfront radiation therapy and non–anthracycline-based chemotherapy has improved treatment and prognosis. This guideline mainly addresses the heterogeneity of clinical features, principles of risk-adapted therapy, and the role and appropriate design of radiation therapy. Radiation therapy methods (including target volume definition, dose and delivery methods) are crucial for optimizing cure for patients with early-stage ENKTCL. The application of the principles of involved site radiation therapy in this lymphoma entity often leads to a more extended clinical target volume (CTV) than in other lymphoma types because it usually presents with primary tumor invasion, multifocal lesions, or extensive submucosal infiltration beyond the macroscopic disease. The CTV varies across different primary sites and is classified mainly into nasal, nonnasal upper aerodigestive tract (UADT), and extra-UADT entities. This review is a consensus of the International Lymphoma Radiation Oncology Group regarding the approach to radiation therapy, target-volume definition, optimal dose, and dose constraints in ENKTCL treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

COVID-19 Vaccine-Induced Radiation Recall Phenomenon

Radiation recall phenomenon (RRP) is an uncommon, late occurring, acute inflammatory skin reaction that emerges in localized areas coincident with previously irradiated radiation therapy (RT) treatment fields. RRP has been known to be triggered by a number of chemotherapy agents. To the best of our knowledge, this report is the first description of RRP after administration of the Pfizer-BioNTech vaccine for COVID-19, or any other currently available vaccine against COVID-19. Acute skin reactions were observed in 2 RT patients with differing timelines of RT and vaccinations. In both cases however, the RRP presented within days of the patient receiving the second dose of vaccine. For each RT course, the treatment planning dosimetry of the radiation fields was compared with the area of the observable RRP. RRP developed within the borders of treatment fields where prescription dose constraints were prioritized over skin sparing. Our observation is currently limited to 2 patients. The actual incidence of RRP in conjunction with Pfizer-BioNTech vaccine or any other vaccine against COVID-19 is unknown. For patients with cancer being treated with radiation with significant dose to skin, consideration should be given to the probability of RRP side effects from vaccinations against COVID-19.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Finite Volume schemes on unstructured grids for non-local models: Application to the simulation of heat transport in plasmas

In the so-called Spitzer-Haerm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer-Haerm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Fluid simulations with atomistic resolution: a hybrid multiscale method with field-wise coupling

We present a new hybrid method for simulating dense fluid systems that exhibit multiscale behaviour, in particular, systems in which a Navier–Stokes model may not be valid in parts of the computational domain. We apply molecular dynamics as a local microscopic refinement for correcting the Navier–Stokes constitutive approximation in the bulk of the domain, as well as providing a direct measurement of velocity slip at bounding surfaces. Our hybrid approach differs from existing techniques, such as the heterogeneous multiscale method (HMM), in some fundamental respects. In our method, the individual molecular solvers, which provide information to the macro model, are not coupled with the continuum grid at nodes (i.e. point-wise coupling), instead coupling occurs over distributed heterogeneous fields (here referred to as field-wise coupling). This affords two major advantages. Whereas point-wise coupled HMM is limited to regions of flow that are highly scale-separated in all spatial directions (i.e. where the state of non-equilibrium in the fluid can be adequately described by a single strain tensor and temperature gradient vector), our field-wise coupled HMM has no such limitations and so can be applied to flows with arbitrarily-varying degrees of scale separation (e.g. flow from a large reservoir into a nano-channel). The second major advantage is that the position of molecular elements does not need to be collocated with nodes of the continuum grid, which means that the resolution of the microscopic correction can be adjusted independently of the resolution of the continuum model. This in turn means the computational cost and accuracy of the molecular correction can be independently controlled and optimised. The macroscopic constraints on the individual molecular solvers are artificial body-force distributions, used in conjunction with standard periodicity. We test our hybrid method on the Poiseuille flow problem for both Newtonian (Lennard-Jones) and non-Newtonian (FENE) fluids. The multiscale results are validated with expensive full-scale molecular dynamics simulations of the same case. Very close agreement is obtained for all cases, with as few as two micro elements required to accurately capture both the Newtonian and non-Newtonian flowfields. Our multiscale method converges very quickly (within 3–4 iterations) and is an order of magnitude more computationally efficient than the full-scale simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Beyond first-order finite element schemes in micromagnetics

Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

New perspectives on superparameterization for geophysical turbulence

This is a research expository paper regarding superparameterization, a class of multi-scale numerical methods designed to cope with the intermittent multi-scale effects of inhomogeneous geophysical turbulence where energy often inverse-cascades from the unresolved scales to the large scales through the effects of waves, jets, vortices, and latent heat release from moist processes. Original as well as sparse space–time superparameterization algorithms are discussed for the important case of moist atmospheric convection including the role of multi-scale asymptotic methods in providing self-consistent constraints on superparameterization algorithms and related deterministic and stochastic multi-cloud parameterizations. Test models for the statistical numerical analysis of superparameterization algorithms are discussed both to elucidate the performance of the basic algorithms and to test their potential role in efficient multi-scale data assimilation. The very recent development of grid-free seamless stochastic superparameterization methods for geophysical turbulence appropriate for “eddy-permitting” mesoscale ocean turbulence is presented here including a general formulation and illustrative applications to two-layer quasigeostrophic turbulence, and another difficult test case involving one-dimensional models of dispersive wave turbulence. This last test case has randomly generated solitons as coherent structures which collapse and radiate wave energy back to the larger scales, resulting in strong direct and inverse turbulent energy cascades.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A thermodynamically compatible splitting procedure in hyperelasticity

A material is hyperelastic if the stress tensor is obtained by variation of the stored energy function. The corresponding 3D mathematical model of hyperelasticity written in the Eulerian coordinates represents a system of 14 conservative partial differential equations submitted to stationary differential constraints. A classical approach for numerical solving of such a 3D system is a geometrical splitting: the 3D system is split into three 1D systems along each spatial direction and solved then by using a Godunov type scheme. Each 1D system has 7 independent eigenfields corresponding to contact discontinuity, longitudinal waves and shear waves. The construction of the corresponding Riemann solvers is not an easy task even in the case of isotropic solids. Indeed, for a given specific energy it is extremely difficult, if not impossible, to check its rank-one convexity which is a necessary and sufficient condition for hyperbolicity of the governing equations. In this paper, we consider a particular case where the specific energy is a sum of two terms. The first term is the hydrodynamic energy depending only on the density and the entropy, and the second term is the shear energy which is unaffected by the volume change. In this case a very simple criterion of hyperbolicity can be formulated. We propose then a new splitting procedure which allows us to find a numerical solution of each 1D system by solving successively three 1D sub-systems. Each sub-system is hyperbolic, if the full system is hyperbolic. Moreover, each sub-system has only three waves instead of seven, and the velocities of these waves are given in explicit form. The last property allows us to construct reliable Riemann solvers. Numerical 1D tests confirm the advantage of the new approach. A multi-dimensional extension of the splitting procedure is also proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗