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Results for “HEAT EQUATION”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Time-stepping DPG formulations for the heat equation

For a wide range of PDEs, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and minimization of the residual in a user-controlled norm, among other appealing features. Research on DPG for transient problems has mainly focused on spacetime discretizations, which has theoretical advantages, but practical costs for computations and software implementations. The sole examination of time-stepping DPG formulations was performed by Führer, Heuer, and Gupta, who applied Rothe’s method to an ultraweak formulation of the heat equation to develop an implicit time-stepping scheme; their work emphasized theoretical results, including error estimates in time and space. Here, we follow Führer, Heuer, and Gupta in examining the heat equation; our focus is on numerical experiments, examining the stability and accuracy of several formulations, including primal as well as ultraweak, and explicit as well as implicit and Crank–Nicolson time-stepping schemes. We are additionally interested in communication-avoiding algorithms, and we therefore include a highly experimental formulation that places all the trace terms on the right-hand side of the equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Heat Equation Neural Simulation

This code solves a steady state heat equation problem on a wire with random walks implemented using a spiking neural algorithm. SAND2020-12194 M

Reeder, Leah↗
NASA NTRS1979

Approximate convective heating equations for hypersonic flows

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Zoby, E. V.↗
DOE OSTI2017

Numerically Solving the Heat Equation

This lecture was presented at the 2017 LANL Parallel Computing Summer Research lecture and it describes the heat equation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Analysis of some fully-discrete algorithms for the one-dimensional heat equation

The present investigation is concerned with a fully discrete accuracy and stability analysis of the one-dimensional heat equation, taking into account the evaluation of two-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices. Schemes of the considered characteristics are not amenable to uncoupled semidiscrete and ordinary differential equation analyses. The obtained results illustrate that superior behavior may be achieved by schemes of the employed type when compared with the performance of the standard one-pass explicit schemes. The key idea in the considered approach is related to the utilization of a reduced-quadrature capacity matrix in the evaluation of the right-hand-side residual.

Hughes, T. J. R.↗
NASA NTRS2000

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Kouatchou, Jules↗
DOE OSTI2025

Heat equations

This dataset consists of 1000 records in a single HDF5 file generated from the simulation code available at: https://github.com/lezahlie/heat_diffusion_simulation. The specific heat equations implemented in that simulation are explained here https://visualpde.com/basic- pdes/heat- equation.html and here https://en.wikipedia.org/wiki/Heat_equation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Kouatchou, Jules↗
NASA NTRS2001

Comparison of Implicit Collocation Methods for the Heat Equation

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Kouatchou, Jules↗
DOE OSTI2018

Heat transfer from glass melt to cold cap: Melting rate correlation equation

Increasing the efficiency of all-electric melters is a hot topic not only in the waste glass melting industry, where the melting rate directly influences the life cycle of the cleanup process, but also in the commercial glass industry, where increasingly stringent environmental regulations and rapid development of renewable energy sources ask for transformation of traditional fossil fuel technology. Batch-to-glass conversion in an all-electric melter proceeds in the cold cap—a layer of reacting and melting material floating on molten glass. The heat transfer into the cold cap is controlled by convection and conduction in the thermal boundary layer on the melt side, and by the properties of the foam layer at the cold cap/melt boundary. An overview of factors affecting heat transfer is presented and assessed using data from laboratory and pilot-scale experiments. The heat flux can be improved by (i) decreasing glass melt viscosity, (ii) decreasing the temperature at which the foam starts to collapse at the cold cap bottom, and (iii) increasing melt convection by bubbling gas into the glass melt under the cold cap. Detailed understanding of the conversion process can guide the formulation of feeds that melt easily and quickly.

Hrma, Pavel↗
NASA NTRS1982

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

Malkus, D. S.↗