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Definition. Generally speaking, Riemann solvers are specific methods for computing the numerical flux across a discontinuity in the Riemann problem. They form an important part of high-resolution schemes; typically the right and left states for the Riemann problem are calculated using some form of nonlinear reconstruction, such as a flux limiter or a WENO method, and then used as the input for ...
Roe solver. The Roe approximate Riemann solver, devised by Phil Roe, is an approximate Riemann solver based on the Godunov scheme and involves finding an estimate for the intercell numerical flux or Godunov flux at the interface between two computational cells and , on some discretised space-time computational domain.
REA was founded by Max Fogiel in 1959 as an educational publisher, concentrating on problems and solutions, or what's known as test preparation today. The company produced the iconic "Problem Solver" series of comprehensive solution guides. The Problem Solver series eventually encompassed over 30 topics with more than 28,000 problem/solution ...
List of unsolved problems in physics. The following is a list of notable unsolved problems grouped into broad areas of physics. [1] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning ...
Sturm–Liouville theory. In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form: for given functions , and , together with some boundary conditions at extreme values of . The goals of a given Sturm–Liouville problem are: To find the λ for which there exists a non ...
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: Yang–Mills Existence and Mass Gap.
The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun. In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles.
For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.
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