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Showing 1 to 19 of 19 for “"Balance Laws"”.
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Discontinuities, Balance Laws, and Material Momentum
… The study entails interrogation of the classical balance laws of momentum, angular momentum, and energy across propagating discontinuities. A major part of this dissertation also concerns itself with a non-classical entity called the ``material momentum''. The balance of material momentum is …
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Scalar Balance Laws with Singular Nonlocal Sources.
North Carolina State University Dissertation Mathematics
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Adjoint-based optimization for hyperbolic balance laws in the presence of discontinuities
… wave patterns that appear in hyperbolic balance laws: contact discontinuities and shocks. These two have very different characteristics in the forward problem and we will see that they require different treatments for the adjoint formulations as well. Specifically, shocks require …
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Numerical methods for advection-diffusion-reaction equations and medical applications
… may include stiff reactive terms, as hyperbolic balance laws with stiff source terms. The resulting systems of hyperbolic balance laws are solved by extending the applicability of existing high-order ADER schemes, including well-balanced and non-conservative schemes. Moreover, we also present a …
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Elastodynamics and wave propagation in fractal media
… is first developed from fractional hydrodynamic laws, and then, boundary value problems are solved analytically and numerically on spherical domains. In the second model, the fractality is direction dependent, thus the designation ``anisotropic''. This model, which implements the concept of …
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Finite volume schemes for hyperbolic-parabolic systems : error estimates
… approximate solutions of systems of hyperbolic balance laws in multi-space dimension. <br>The convergence analysis for the scalar case is well developed, even though <br>not complete up to now. In contrast, very few is known for the case of systems. <br>Following the ideas of J.P. Vila and P. …
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Coupled Elastic-Plastic Thermomechanically Assisted Diffusion: Theory Development, Numerical Implementation, and Application
… mechanics and classical plasticity theory, balance laws and constitutive equations are derived for a continuum composed of an immobile, but deformable, parent material and a dilute mobile constituent. The resulting equations are cast into a finite element formulation for incorporation into a …
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A coupled, two-phase fluid-sediment material model and mixture theory implemented using the material point method
… is developed from the integral form of the basic balance laws for two-phase mixtures. This model is formulated to capture the (i) viscous inertial rheology of wet grains under steady shear, (ii) the critical state behavior of granular materials under shear, (iii) the viscous thickening of fluid …
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A holistic multi-scale mathematical model of the murine extracellular fluid systems and study of the brain interactive dynamics
… numerical method for systems of hyperbolic balance laws in networks, based on a new implicit solver for the junction-generalized Riemann problem. The resulting ADER scheme can deal with stiff source terms and can be applied to non-linear systems of hyperbolic balance laws in domains …
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Geometric electroelasticity
… electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as …
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On a Proposal for a Continuum With Microstructure
… take place spontaneously according to the balance laws of effective mass and momentum. When the constitutive equations are subjected to the requirements of invariance, familiar statements from dislocation dynamics are deduced. When plastic strain and yield are identified in terms of the …
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Renormalization analysis of continuum models on fractal domains
… of fractional integrals employed to state global balance laws. In effect, the governing equations are cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing …
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Enhanced Constitutive Theories for Classical Thermoviscoelastic Polymeric Fluids
… polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The …
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Solving the system of Radiation Magnetohydrodynamics : for solar physical simulations in 3d
… solar photosphere. It is a non--linear system of balance laws derived from the Euler equations of gas dynamics and the Maxwell equations; the energy transport through radiation is also included in the model. <br>The starting point of our presentation is a standard explicit first and second order …
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A Spacetime, Balance-Law Formulation of Coupled Atomistic and Continuum Dynamics for Solids
… simulations of solids that enforces these balance laws on the atom/element level while minimizing spurious reflections. The coupled formulation is composed of the continuum spacetime discontinuous Galerkin (SDG) method and the mathematically consistent, time finite element, atomistic …
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Shock Physics in Compressible Solids
… framework is constructed using conservation and balance laws (CBL) of classical continuum mechanics (CCM) and constitutive theories derived from the entropy inequality and the representation theorem. The models incorporate finite deformation and finite strain physics, making them essential for …
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An Approximation for the Twenty-One-Moment Maximum-Entropy Model of Rarefied Gas Dynamics
… offers models described by hyperbolic systems of balance laws. In particular, the twenty-one moment model of the maximum-entropy hierarchy offers a hyperbolic treatment of viscous flows exhibiting heat transfer. This twenty-one moment model has the ability to provide accurate solutions where the …
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Constitutive modeling of Cu-Al-Ni shape memory alloys
… the "kinetics"). It is well known that classical balance laws are insufficient for a complete description of the behavior of materials undergoing phase transformations. The classical continuum theory describes the bulk regions (regions away from the interfaces) in a satisfactory manner but leaves …
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Boundary-value problems for transversely isotropic hyperelastic solids
… fundamental stress principles as well as balance laws; those also being appropriately specialized for material bodies under the state of equilibrium, i.e. for static problems. Description of the governing constitutive theory for Cauchy elastic isotropic and transversely isotropic solids …