Multi-thread band matrix solver for well system fluid flow modeling

A non-transitory computer-readable medium storing instructions that, when executed by data processing apparatus, perform operations comprising:

• performing a first elimination on an upper part of a band matrix, the band matrix including flow variable coefficients based on governing flow equations representing well system fluid flow in a subterranean region, the upper part of the band matrix including a first subset of the flow variable coefficients corresponding to a first subset of flow variables in the governing flow equations;
• performing, in parallel with the first elimination, a second elimination on a lower part of the band matrix, the lower part of the band matrix including a second subset of flow variable coefficients corresponding to a second subset of the flow variables in the governing flow equations;
• and
• solving an intermediate part of the band matrix, the intermediate part of the band matrix including other flow variable coefficients of the band matrix, wherein the intermediate part comprises at least ρ rows, ρ being a bandwidth of the band matrix.

A flow modeling system comprising one or more computers that include:

• memory operable to store a band matrix that includes flow variable coefficients based on governing flow equations representing well system fluid flow in a subterranean region;
• and
• data processing apparatus operable to:
• perform a first elimination on an upper part of the band matrix, the upper part of the band matrix including a first subset of the flow variable coefficients corresponding to a first subset of flow variables in the governing flow equations;
• perform, in parallel with the first elimination, a second elimination on a lower part of the band matrix, the lower part of the band matrix including a second subset of flow variable coefficients corresponding to a second subset of the flow variables in the governing flow equations;
• and
• solve an intermediate part of the band matrix, the intermediate part of the band matrix including other flow variable coefficients of the band matrix, wherein the intermediate part comprises at least ρ rows, ρ being a bandwidth of the band matrix.